{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9257006d-f611-4e5a-8c78-b796cc28452b",
   "metadata": {},
   "source": [
    "Chapter 24\n",
    "# PageRank算法\n",
    "Book_6《数据有道》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "20ad3aca-648d-43dc-856e-bb1f2e700606",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0f14b8dc-f8fe-4ee8-8a66-a392e6c71e7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "directed_G = nx.DiGraph()\n",
    "# 创建有向图的实例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7cac13da-c635-4b19-bb96-6183926fbb47",
   "metadata": {},
   "outputs": [],
   "source": [
    "directed_G.add_nodes_from(['a', 'b', 'c', 'd', 'e', 'f'])\n",
    "# 添加多个顶点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ea20476a-eeb1-4d20-a9a9-7ce0c2462f0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 添加几组有向边\n",
    "directed_G.add_edges_from([('a','b'),('a','c'),('a','d'),\n",
    "                           ('a','e'),('a','f')])\n",
    "directed_G.add_edges_from([('b','d'),('b','e')])\n",
    "directed_G.add_edges_from([('c','a'),('c','d'),('c','e')])\n",
    "directed_G.add_edges_from([('d','b'),('d','e')])\n",
    "directed_G.add_edges_from([('e','a')])\n",
    "directed_G.add_edges_from([('f','b'),('f','c'),('f','e')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "256dc393-e38f-49da-aec8-145ee053a5cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = nx.circular_layout(directed_G)\n",
    "node_color = ['purple', 'blue', 'green', 'orange', 'red', 'pink']\n",
    "\n",
    "# 可视化\n",
    "plt.figure(figsize = (6,6))\n",
    "nx.draw_networkx(directed_G, \n",
    "                 pos = pos,\n",
    "                 node_color = node_color,\n",
    "                 node_size = 180)\n",
    "plt.savefig('网页之间关系的有向图.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "25fb57fb-1a52-4a6d-a675-e596789d7c76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 1, 1],\n",
       "       [0, 0, 0, 1, 1, 0],\n",
       "       [1, 0, 0, 1, 1, 0],\n",
       "       [0, 1, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 1, 0, 1, 0]], dtype=int32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 邻接矩阵\n",
    "A = nx.adjacency_matrix(directed_G).todense()\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5edc50da-14ff-47e0-ae94-0baf711c31d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a', 'b', 'c', 'd', 'e', 'f']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(directed_G.nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b5763ed-d3e6-40ae-bfec-95885a3b6385",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8df77ee0-8b82-4cf8-8e34-938a6828e2dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A, cmap = 'Blues', \n",
    "            annot = True, fmt = '.0f',\n",
    "            xticklabels = list(directed_G.nodes), \n",
    "            yticklabels = list(directed_G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('邻接矩阵.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ad13a0f-b09d-44d5-93d5-b17ee8deb283",
   "metadata": {},
   "source": [
    "## 转移矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bb7d9b49-bbba-405b-87c1-7567bbc11e3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "deg_out = A.sum(axis=1)[:, np.newaxis]\n",
    "# 节点出度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7933d222-bb3d-4851-8902-bb2f41bb5401",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GEbjFitmzZys5OVkRERGKiIhQSkqKPv74Y7/r5+TkyDAMnyU0NNTy+VJJAgCCXtu2bTV9+nQlJCTI6/Xq7bff1tChQ7V9+3Z17979kttERERo7969VZ9rUgWTJAEApgWy3erxeOTxeHzGXC6XXC7XResOGTLE5/OLL76o2bNn69NPP/WbJA3DUExMzBXFSLsVAGBaINutbrdbkZGRPovb7a42hoqKCi1cuFDl5eVKSUnxu15ZWZk6dOigdu3aaejQodq1a5fl86WSBADYIjs7W1lZWT5jl6oif7Bjxw6lpKTo7Nmzatq0qRYvXqxu3S792sHExES9+eabSk5OVmlpqX7zm98oNTVVu3btUtu2bU3HSJIEAJgWEsB2q7/Wqj+JiYnKz89XaWmpPvjgAz388MNat27dJRNlSkqKT5WZmpqqrl27au7cuZo2bZrpY5IkAQCm2XkHSOPGjRUfHy9J6tmzpzZv3qxZs2Zp7ty51W7bqFEj3XTTTSooKLB0TK5JAgDqpcrKyosm/vhTUVGhHTt2KDY21tIxqCQBAKbZ9TCB7OxsDRo0SO3bt9fp06e1YMECrV27VitXrpQkpaenKy4urmriz9SpU9WrVy/Fx8fr5MmTmjFjhg4dOqRHHnnE0nFJkgAA00JsarcePXpU6enpKioqUmRkpJKTk7Vy5UoNGDBAklRYWKiQkH82R0+cOKFRo0apuLhYzZs3V8+ePZWbm+t3oo8/htfr9Qb0TGrIMAw98T+77Q6jzrz+4Pf/oYLk6wcAU+6d81nA9rX8sVsDtq/awjVJAAD8oN0KADDNYc83d2aS7NOpmfp0aq6oaxpJkopOe/Txnm+0u6Tc5sgAILgZclaWdGSSPHHmgpbuOqqjZedkGIZuax+pn/dqp+lr9qvo9Dm7wwMABAlHJsmdxWU+n/9v9zH16dRcHaPCSJIAcBl2zW61iyOT5L8yJPWIi1DjBoYOfHvG7nAAIKg57aXLNUqSbrdb0dHR+u///m+f8TfffFPHjh3TxIkTAxJcbWoT4dL4vh3VMMSQ50Kl5m86rGKqSADAv6jRLSBz585Vly5dLhrv3r275syZU+32Ho9Hp06d8lnqWslpj9xr9mvGuoP624ET+lnPNooJb1zncQBAfRLIV2XVBzVKksXFxZd8/l2rVq1UVFRU7faXeodYXavwSsfKz+urk2f1v7uP6etSj+64NqrO4wCA+iTEMAK21Ac1SpLt2rXTxo0bLxrfuHGj2rRpU+322dnZKi0t9VnsZhhSQ6ddkQYAXFaNrkmOGjVKY8eO1fnz53XnnXdKklavXq2nn35aTz31VLXbW32HWKDd362VdpeU6dszFxTaMEQ3t41QQstr9NrGr2yLCQDqg3pSAAZMjZLkhAkTdPz4cT3xxBM6d+77yS6hoaGaOHGisrOzAxpgbQh3NVR6zzaKCG2osxcq9XWpR69t/Ep7jvEwAQC4HGa3mmAYhn79619r8uTJ+vzzzxUWFqaEhARbq0Mr/rS9+uumAICLOSxHXtl9kk2bNtUtt9wSqFgAAAgqjn+YAADAvPoyKzVQSJIAANOclSJ5nyQAAH5RSQIATGN2KwAAfjjtmSu0WwEA8INKEgBgGu1WAAD8cFiOpN0KAIA/VJIAANNotwIA4IfTZreSJAEApjmtkuSaJAAAflBJAgBMc1YdSZIEAFjgtLeA0G4FAMAPKkkAgGkOKyRJkgAA85jdCgAAJFFJAgAscFghSZIEAJjH7FYAAILM7NmzlZycrIiICEVERCglJUUff/zxZbdZtGiRunTpotDQUF1//fVavny55eOSJAEAphlG4BYr2rZtq+nTp2vr1q3asmWL7rzzTg0dOlS7du265Pq5ubkaNmyYMjIytH37dqWlpSktLU07d+60dr5er9drLdTa4bQZUz8Ikq8fAEwZvfjzgO3rlXs7y+Px+Iy5XC65XC5T20dFRWnGjBnKyMi46GcPPfSQysvLtWzZsqqxXr166cYbb9ScOXNMx0glCQAwLSSAi9vtVmRkpM/idrurjaGiokILFy5UeXm5UlJSLrlOXl6e+vfv7zM2cOBA5eXlWTrfoJq4k/vlCbtDqDOpCc3tDgEAbJWdna2srCyfsctVkTt27FBKSorOnj2rpk2bavHixerWrdsl1y0uLlZ0dLTPWHR0tIqLiy3FGFRJEgAQ3AJ5acxKa1WSEhMTlZ+fr9LSUn3wwQd6+OGHtW7dOr+JMhBIkgAA0+x86XLjxo0VHx8vSerZs6c2b96sWbNmae7cuRetGxMTo5KSEp+xkpISxcTEWDom1yQBAPVSZWXlRRN/fpCSkqLVq1f7jK1atcrvNUx/qCQBAKbZVUlmZ2dr0KBBat++vU6fPq0FCxZo7dq1WrlypSQpPT1dcXFxVRN/MjMz1bdvX82cOVODBw/WwoULtWXLFs2bN8/ScUmSAADT7Lpd7+jRo0pPT1dRUZEiIyOVnJyslStXasCAAZKkwsJChYT8szmampqqBQsWaNKkSXr22WeVkJCgJUuWKCkpydJxg+o+SSfObg2Srx8ATHnq//YGbF8zhyQGbF+1hUoSAGCanRN37ECSBACY5rSHozG7FQAAP6gkAQCmOe1VWSRJAIBpTms/kiQBAKY5rJB03C8FAACYRiUJADCNa5IAAPjhsBxJuxUAAH+oJAEApvHEHQAA/HDaNUnarQAA+EElCQAwzWGFJEkSAGCe065J0m4FAMAPKkkAgGmGnFVKkiQBAKY5rd3qyCS57P0cbc1dq6LDh9SosUvxXa/Xf44co9i2HewODQCCmtOSpCOvSe7ZsV13Dv4PTZ75R0341e9VceGCfjPpSXnOnrE7NABAEHFkJTl+2iyfz49kPacnf3qPDhbsUWLSTTZFBQDBz3DYPSCOTJL/7kx5mSSpSdMImyMBgODmtHar6SSZlZVleqevvPLKZX/u8Xjk8XhM7682VVZWasG83yqhW7LadrzW7nAAAEHEdJLcvn27z+dt27bpwoULSkxMlCR98cUXatCggXr27Fntvtxut1544QWLodaOd2fP0OFD+/XLGXPtDgUAgp7Duq3mk+Rf//rXqr+/8sorCg8P19tvv63mzZtLkk6cOKGRI0eqT58+1e4rOzv7oso0MjLSbCgB8+7sGfr7ZxuU/eu5imoZXefHB4D6xmkPODe8Xq/X6kZxcXH65JNP1L17d5/xnTt36u6779aRI0esB2IYyv3yhOXtasLr9eq9Ob/R1rx1esb9umLi2tfJcf9VakLzqlgAoL743d8OBGxfY/t0Cti+akuNJu6cOnVKx44du2j82LFjOn369BUHVdvefX2G8tatVObkGQoNa6KT3x6XJF3TpIkau0Jtjg4AghcTd0x44IEHNHLkSM2cOVO33nqrJGnTpk2aMGGCHnzwwYAGWBvWLP9QkjT9mcd9xjPGTlafAffZERIA1AsO67bWLEnOmTNH48eP109/+lOdP3/++x01bKiMjAzNmDEjoAHWhpyPNtkdAgCgHqjRNckflJeXa9++fZKka6+9Vk2aNKl5IHV4TTIYcE0SQH302saDAdvX6Ns7BmxfteWKHibQpEkTJScnByoWAECQo90KAIAfTpu448gHnAMAYAaVJADANKc9TIAkCQAwzWE5knYrACD4ud1u3XLLLQoPD1fr1q2VlpamvXv3XnabnJwcGYbhs4SGWntgDEkSAGBaiGEEbLFi3bp1Gj16tD799FOtWrVK58+f1913363y8vLLbhcREaGioqKq5dChQ5aOS7sVAGCaXe3WFStW+HzOyclR69attXXrVv3oRz/yu51hGIqJianxcakkAQC28Hg8OnXqlM9i9l3DpaWlkqSoqKjLrldWVqYOHTqoXbt2Gjp0qHbt2mUpRpIkAMC0kAAubrdbkZGRPovb7a42hsrKSo0dO1a33367kpKS/K6XmJioN998U0uXLtV7772nyspKpaam6vDhw6bP94oeSxdIPJYOAILf21u+Cti+fnJ964sqR5fLJZfLddntHn/8cX388cfasGGD2rZta/p458+fV9euXTVs2DBNmzbN1DZckwQA2MJMQvx3Y8aM0bJly7R+/XpLCVKSGjVqpJtuukkFBQWmt6HdCgAwzQjgYoXX69WYMWO0ePFirVmzRp06WX9hc0VFhXbs2KHY2FjT21BJAgBMs+uJO6NHj9aCBQu0dOlShYeHq7i4WJIUGRmpsLAwSVJ6erri4uKqrmtOnTpVvXr1Unx8vE6ePKkZM2bo0KFDeuSRR0wflyQJADDNrgfuzJ49W5LUr18/n/G33npLI0aMkCQVFhYqJOSfDdITJ05o1KhRKi4uVvPmzdWzZ0/l5uaqW7dupo/LxB2bMHEHQH30p63mZ4ZWZ3hPa9cU7UAlCQAwzWnPbiVJAgBMMxyWJZndCgCAH1SSAADTnFZZkSQBAKbRbgUAAJKoJAEAFjirjgyyJPnDvYMAgOBEuxUAAEgKskryzHnnPH0mrJGzfhsDcHVwWmUVVEkSABDcnNZuJUkCAExzVop0XuUMAIBpVJIAANMc1m0lSQIAzAtxWMOVdisAAH5QSQIATKPdCgCAHwbtVgAAIFFJAgAsoN0KAIAfzG4FAACSqCQBABbQbgUAwA+SJAAAfnALCAAAkEQlCQCwIMRZhSRJEgBgHu1WAAAgiUoSAGABs1sBAPCDdisAAJBEJQkAsIDZrQAA+EG71SG2btmsXzzxmPr3660buidqzeq/2B0SACDIODZJnjnznRITE5U96Xm7QwGAesMwArdY4Xa7dcsttyg8PFytW7dWWlqa9u7dW+12ixYtUpcuXRQaGqrrr79ey5cvt3RcxybJ3n36akzmON3Vf4DdoQBAvWEEcLFi3bp1Gj16tD799FOtWrVK58+f1913363y8nK/2+Tm5mrYsGHKyMjQ9u3blZaWprS0NO3cudP8+Xq9Xq/FWCVJf/vb3zR37lzt27dPH3zwgeLi4vTuu++qU6dO6t27t+X9GYahM+drFMoVu6F7on77+9d051396+yYYY2+/ydSw68fAGyRV3AyYPtKiW9W422PHTum1q1ba926dfrRj350yXUeeughlZeXa9myZVVjvXr10o033qg5c+aYOk6NKskPP/xQAwcOVFhYmLZv3y6PxyNJKi0t1UsvvVTt9h6PR6dOnfJZAADOcqlc8EM+qU5paakkKSoqyu86eXl56t/ft/gZOHCg8vLyTMdYoyT5q1/9SnPmzNH8+fPVqFGjqvHbb79d27Ztq3Z7t9utyMhInwUAEPwC2W69VC5wu93VxlBZWamxY8fq9ttvV1JSkt/1iouLFR0d7TMWHR2t4uJi0+dbo1tA9u7de8nyNjIyUidPnqx2++zsbGVlZV20LQAgyAXwDpBL5QKXy1XtdqNHj9bOnTu1YcOGwAXjR42SZExMjAoKCtSxY0ef8Q0bNqhz587Vbu9yuUx9EQCAq1dNcsGYMWO0bNkyrV+/Xm3btr3sujExMSopKfEZKykpUUxMjOnj1ajdOmrUKGVmZmrTpk0yDENHjhzRn/70J40fP16PP/54TXZZ574rL9eezz/Xns8/lyR9ffiw9nz+uYqOHLE5MgAIXkYA/1jh9Xo1ZswYLV68WGvWrFGnTp2q3SYlJUWrV6/2GVu1apVSUlLMn29NZrd6vV699NJLcrvd+u677yR9/xvB+PHjNW3aNKu7+z6QOp7duvmzTXpkZPpF4/cPfUDTXppe68dndiuA+uiz/aUB29etnc1fZnviiSe0YMECLV26VImJiVXjkZGRCgsLkySlp6crLi6u6rpmbm6u+vbtq+nTp2vw4MFauHChXnrpJW3btu2y1zL/VY1vAZGkc+fOqaCgQGVlZerWrZuaNm1a013ZeguIHUiSAOoju5Kk4efpA2+99ZZGjBghSerXr586duyonJycqp8vWrRIkyZN0sGDB5WQkKCXX35Z9957r/njXkmSDCSSJAAEv80BTJK3WEiSduEB5wAA85z1fHPnPpYOAIDqUEkCAExz2quySJIAANOsvr2jviNJAgBMc1iO5JokAAD+UEkCAMxzWClJkgQAmOa0iTu0WwEA8INKEgBgGrNbAQDww2E5knYrAAD+UEkCAMxzWClJkgQAmMbsVgAAIIlKEgBgAbNbAQDww2E5kiQJALDAYVmSa5IAAPhBJQkAMM1ps1tJkgAA05w2cYd2KwAAflBJAgBMc1ghGVxJMqyR075+AKhnHPa/adqtAAD4EVSV5BP/s9vuEOrM6w92szsEALCM2a0AAPjB7FYAACCJShIAYIHDCkmSJADAAodlSZIkAMA0p03c4ZokAAB+UEkCAExz2uxWkiQAwDSH5UjarQAA+EOSBACYZwRwsWD9+vUaMmSI2rRpI8MwtGTJksuuv3btWhmGcdFSXFxs6bgkSQCAaUYA/1hRXl6uG264Qa+99pql7fbu3auioqKqpXXr1pa255okACDoDRo0SIMGDbK8XevWrdWsWbMaH5dKEgBgmmEEbvF4PDp16pTP4vF4AhrvjTfeqNjYWA0YMEAbN260vD1JEgBgWiAvSbrdbkVGRvosbrc7IHHGxsZqzpw5+vDDD/Xhhx+qXbt26tevn7Zt22ZpP4bX6/UGJKIrZBiGI1+VFSRfPwCYcvCbswHbV2y4cVHl6HK55HK5LrudYRhavHix0tLSLB2vb9++at++vd59913T23BNEgBgXgBvlDSTEAPp1ltv1YYNGyxtQ5IEAJhWn5/dmp+fr9jYWEvbkCQBAKbZ9Vi6srIyFRQUVH0+cOCA8vPzFRUVpfbt2ys7O1tff/213nnnHUnS7373O3Xq1Endu3fX2bNn9cYbb2jNmjX65JNPLB2XJAkACHpbtmzRHXfcUfU5KytLkvTwww8rJydHRUVFKiwsrPr5uXPn9NRTT+nrr7/WNddco+TkZP3lL3/x2YcZTNyxCRN3ANRHX30buFs02kXV3fXImqKSBACY5rS3gHCfJAAAflBJAgAscFYp6cgk2adTM/Xp1FxR1zSSJBWd9ujjPd9od0m5zZEBQHBzWrvVkUnyxJkLWrrrqI6WnZNhGLqtfaR+3qudpq/Zr6LT5+wODwAQJByZJHcWl/l8/r/dx9SnU3N1jAojSQLAZTiskHRmkvxXhqQecRFq3MDQgW/P2B0OAAQ12q2X8I9//ENJSUkKCQnMZFiPxxPw16FY1SbCpfF9O6phiCHPhUrN33RYxVSRAIB/YSrr3XTTTfrmm28kSZ07d9bx48ev6KCXej1KXSs57ZF7zX7NWHdQfztwQj/r2UYx4Y3rPA4AqE+MAP6pD0wlyWbNmunAgQOSpIMHD6qysvKKDpqdna3S0lKfpa5VeKVj5ef11cmz+t/dx/R1qUd3XBtV53EAQL0SyBdK1gOm2q0//vGP1bdvX8XGxsowDN18881q0KDBJdfdv39/tfur69ejmGEYUsOQevJfDQBs4rT/S5pKkvPmzdODDz6ogoICPfnkkxo1apTCw8NrO7Zac3+3VtpdUqZvz1xQaMMQ3dw2Qgktr9FrG7+yOzQAQBAxPbv1nnvukSRt3bpVmZmZ9TpJhrsaKr1nG0WENtTZC5X6utSj1zZ+pT3HeJgAAFwOs1ur8dZbb9VGHHXqT9uL7A4BAOql+jLhJlB4wDkAAH44/mECAAALnFVIkiQBAOY5LEfSbgUAwB8qSQCAacxuBQDAD2a3AgAASVSSAAALnNZupZIEAMAPKkkAgGlUkgAAQBKVJADAAqfNbiVJAgBMo90KAAAkUUkCACxwWCFJkgQAWOCwLEm7FQAAP6gkAQCmMbsVAAA/mN0KAAAkUUkCACxwWCFJkgQAWOCwLEm7FQBgmhHAP1asX79eQ4YMUZs2bWQYhpYsWVLtNmvXrlWPHj3kcrkUHx+vnJwcy+dLkgQABL3y8nLdcMMNeu2110ytf+DAAQ0ePFh33HGH8vPzNXbsWD3yyCNauXKlpeMaXq/XW5OAA81w2pSp/y9Ivn4AMOXshcDty6jwyOPx+Iy5XC65XK7Lb2cYWrx4sdLS0vyuM3HiRH300UfauXNn1dhPfvITnTx5UitWrDAdY9BUkl6v15bl7Nmzev7553X27Flbjm8Hj8ejKVOmXPSP82rnxPN24jlLnHdtnndow8AtbrdbkZGRPovb7Q5InHl5eerfv7/P2MCBA5WXl2dpP0FTSdrl1KlTioyMVGlpqSIiIuwOp0448ZwlZ563E89Z4rzry3l7PLVXSV533XUaOXKksrOzq8aWL1+uwYMH67vvvlNYWJipGJndCgCwhZmEaLegabcCABAoMTExKikp8RkrKSlRRESE6SpSIkkCAK5CKSkpWr16tc/YqlWrlJKSYmk/jk+SLpdLzz//fNCX/IHkxHOWnHneTjxnifO+Gs+7rKxM+fn5ys/Pl/T9LR75+fkqLCyUJGVnZys9Pb1q/ccee0z79+/X008/rT179uj111/X+++/r3Hjxlk6ruMn7gAAgt/atWt1xx13XDT+8MMPKycnRyNGjNDBgwe1du1an23GjRun3bt3q23btpo8ebJGjBhh6bgkSQAA/HB8uxUAAH9IkgAA+EGSBADAD5Kkg/Tr109jx461OwzYiH8DVy+v16tHH31UUVFRMgyjahYorgxP3AGAq8CKFSuUk5OjtWvXqnPnzmrZsqXdIV0VSJIAcBXYt2+fYmNjlZqaancoVxXHtltXrFih3r17q1mzZmrRooXuu+8+7du3z+6wat2FCxc0ZswYRUZGqmXLlpo8ebIjXtdVWVmpl19+WfHx8XK5XGrfvr1efPFFu8OqVeXl5UpPT1fTpk0VGxurmTNn2h1SrausrJTb7VanTp0UFhamG264QR988IHdYdW6ESNG6Be/+IUKCwtlGIY6duxod0hXDccmyfLycmVlZWnLli1avXq1QkJC9MADD6iystLu0GrV22+/rYYNG+qzzz7TrFmz9Morr+iNN96wO6xal52drenTp2vy5MnavXu3FixYoOjoaLvDqlUTJkzQunXrtHTpUn3yySdau3attm3bZndYtcrtduudd97RnDlztGvXLo0bN07/9V//pXXr1tkdWq2aNWuWpk6dqrZt26qoqEibN2+2O6Srhxder9frPXbsmFeSd8eOHXaHUmv69u3r7dq1q7eysrJqbOLEid6uXbvaGFXtO3XqlNflcnnnz59vdyh15vTp097GjRt733///aqx48ePe8PCwryZmZn2BVaLzp49673mmmu8ubm5PuMZGRneYcOG2RRV3fntb3/r7dChg91hXHUcW0l++eWXGjZsmDp37qyIiIiq9sQPzwG8WvXq1UuGYVR9TklJ0ZdffqmKigobo6pdn3/+uTwej+666y67Q6kz+/bt07lz53TbbbdVjUVFRSkxMdHGqGpXQUGBvvvuOw0YMEBNmzatWt555x1HXEpB7XDsxJ0hQ4aoQ4cOmj9/vtq0aaPKykolJSXp3LlzdoeGALPyWhzUX2VlZZKkjz76SHFxcT4/uxof+I264chK8vjx49q7d68mTZqku+66S127dtWJEyfsDqtObNq0yefzp59+qoSEBDVo0MCmiGpfQkKCwsLCLnptztXs2muvVaNGjXz+e584cUJffPGFjVHVrm7dusnlcqmwsFDx8fE+S7t27ewOD/WUIyvJ5s2bq0WLFpo3b55iY2NVWFioZ555xu6w6kRhYaGysrL085//XNu2bdMf/vCHq37WY2hoqCZOnKinn35ajRs31u23365jx45p165dysjIsDu8WtG0aVNlZGRowoQJatGihVq3bq1f/vKXCgm5en8vDg8P1/jx4zVu3DhVVlaqd+/eKi0t1caNGxUREaGHH37Y7hBRDzkySYaEhGjhwoV68sknlZSUpMTERP3+979Xv3797A6t1qWnp+vMmTO69dZb1aBBA2VmZurRRx+1O6xaN3nyZDVs2FDPPfecjhw5otjYWD322GN2h1WrZsyYobKyMg0ZMkTh4eF66qmnVFpaandYtWratGlq1aqV3G639u/fr2bNmqlHjx569tln7Q4N9RSvygIAwI+rt/cCAMAVIkkCAOAHSRIAAD9IkgAA+EGSBADAD5IkAAB+kCQBAPCDJAkAgB8kSQAA/CBJAgDgB0kSAAA//h9VGJaNxAC3PQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(deg_out, cmap = 'Blues', \n",
    "            annot = True, fmt = '.0f',\n",
    "            xticklabels = list(directed_G.nodes), \n",
    "            yticklabels = list(directed_G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('节点出度.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5b341a0d-4c2f-4d86-8762-4faa7bca8921",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_T = A /  deg_out\n",
    "# 邻接矩阵的行归一化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a611d6af-6ff7-408b-95e4-b4a2b776d875",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = T_T.T\n",
    "# 转置获得转移矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a74878fb-d343-493f-bfab-7e21a08d64f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T.sum(axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e646e6b1-2ae3-4f0c-a76f-5b6040d682b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(T, cmap = 'Blues', \n",
    "            annot = True, fmt = '.3f',\n",
    "            xticklabels = list(directed_G.nodes), \n",
    "            yticklabels = list(directed_G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('转移矩阵.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0604dddf-163e-4f07-b72f-454567dde407",
   "metadata": {},
   "source": [
    "## 幂迭代"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "987f3f3c-26bd-4e72-9dad-34dac743a88c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 自定义函数幂迭代\n",
    "\n",
    "def power_iteration(T_, num_iterations: int, L2_norm = False):\n",
    "    \n",
    "    # 初始状态\n",
    "    r_k = np.ones((len(T_),1))/len(T_)\n",
    "    r_k_iter = r_k\n",
    "\n",
    "    for _ in range(num_iterations):\n",
    "        \n",
    "        # 矩阵乘法 T @ r\n",
    "        r_k1 = T_ @ r_k\n",
    "        \n",
    "        if L2_norm:\n",
    "            # 计算L2范数\n",
    "            r_k1_norm = np.linalg.norm(r_k1)\n",
    "\n",
    "            # L2范数单位化\n",
    "            r_k = r_k1 / r_k1_norm\n",
    "        else:\n",
    "            # 归一化\n",
    "            r_k = r_k1 / r_k1.sum()\n",
    "        \n",
    "        # 记录迭代过程结果\n",
    "        r_k_iter = np.column_stack((r_k_iter,r_k))\n",
    "\n",
    "    return r_k,r_k_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "647b936d-6292-4de4-b391-1c0ffa396469",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 调用自行函数完成幂迭代\n",
    "r_k,r_k_iter = power_iteration(T, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f33af23e-96c3-43ec-a757-a57ef8ef1814",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.28662424],\n",
       "       [0.1571125 ],\n",
       "       [0.0764331 ],\n",
       "       [0.16135882],\n",
       "       [0.2611465 ],\n",
       "       [0.05732483]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b2049064-a162-489a-ba2c-6df5e45a2628",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a', 'b', 'c', 'd', 'e', 'f']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ca6bc294-a266-422d-ba4c-b9ca59f3499e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 可视化幂迭代过程\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "for i,node_i in zip(range(len(node_color)),list(directed_G.nodes)):\n",
    "    ax.plot(r_k_iter[i,:], color = node_color[i], label = node_i)\n",
    "ax.set_xlim(0,20)\n",
    "ax.set_ylim(0,0.4)\n",
    "ax.set_xlabel('Iteration')\n",
    "ax.set_ylabel('PageRank')\n",
    "ax.legend(loc = 'upper right')\n",
    "plt.savefig('幂迭代.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "626879c0-af41-466f-a132-066aa8d06364",
   "metadata": {},
   "source": [
    "## 特征值分解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "224c5dd8-8908-493d-aa28-0eac10a17ab6",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenValues, eigenVectors = np.linalg.eig(T)\n",
    "\n",
    "idx = eigenValues.argsort()[::-1]   \n",
    "eigenValues = eigenValues[idx]\n",
    "eigenVectors = eigenVectors[:,idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "00c46308-8803-45cf-ae40-354b5224dc8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.00000000e+00+0.j        , -4.33680869e-17+0.j        ,\n",
       "       -5.30003573e-02+0.j        , -2.23499821e-01+0.39961234j,\n",
       "       -2.23499821e-01-0.39961234j, -5.00000000e-01+0.j        ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenValues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1fb4618f-3d78-418f-bb29-5c3073b35476",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2866242 , 0.15711253, 0.07643312, 0.16135881, 0.2611465 ,\n",
       "       0.05732484])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0 = eigenVectors[:,0]\n",
    "v0 = v0.real\n",
    "# -v0/np.linalg.norm(v0)\n",
    "v0/v0.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab5ec7b2-6a1e-4e4d-9e77-83418de8d813",
   "metadata": {},
   "source": [
    "## 修改有向图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "30da5cb4-4833-4e61-a78b-c8f3806fceef",
   "metadata": {},
   "outputs": [],
   "source": [
    "directed_G_2 = directed_G.copy()\n",
    "directed_G_2.remove_edge('e','a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "251284a2-1595-41c9-9f8e-151b9a9fa5b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 可视化\n",
    "plt.figure(figsize = (6,6))\n",
    "nx.draw_networkx(directed_G_2, \n",
    "                 pos = pos,\n",
    "                 node_color = node_color,\n",
    "                 node_size = 180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "a864636e-7d29-48c3-8adf-5486f3c82d44",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_2 = nx.adjacency_matrix(directed_G_2).todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "04fc8da1-f4bf-47b0-820e-430277749513",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 1, 1],\n",
       "       [0, 0, 0, 1, 1, 0],\n",
       "       [1, 0, 0, 1, 1, 0],\n",
       "       [0, 1, 0, 0, 1, 0],\n",
       "       [0, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 1, 0, 1, 0]], dtype=int32)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "c412bc9b-b8d1-42ba-9c55-27de25ab4f43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A_2, cmap = 'Blues', \n",
    "            annot = True, fmt = '.0f',\n",
    "            xticklabels = list(directed_G.nodes), \n",
    "            yticklabels = list(directed_G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('邻接矩阵，删除ea.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "e2ec39d8-7e06-45b3-8f6e-3645852bd2c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\james\\AppData\\Local\\Temp\\ipykernel_9644\\1677233325.py:2: RuntimeWarning: invalid value encountered in true_divide\n",
      "  T_T = A /  A.sum(axis=1)[:, np.newaxis]\n"
     ]
    }
   ],
   "source": [
    "def A_2_T(A):\n",
    "    T_T = A /  A.sum(axis=1)[:, np.newaxis]\n",
    "    T = T_T.T\n",
    "    T[np.isnan(T)] = 0\n",
    "    return T\n",
    "\n",
    "T_2 = A_2_T(A_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "d7fb0bf2-bdc7-476e-9d5e-2078aad1c0be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UNYCWBC2EEMI8yBS3EEIIIRqcjKCFEEKYBaWNoCVBCyGEMAtKS9AyxS2EEMI8qEy41VJkZCR+fn7Y2toSEhJCTExMjY7btm0bKpWKUaNG1fqckqCFEEKIO9i+fTthYWEsWLCA2NhYunTpwogRI0hNTb3jcZcvX+bFF19kwIABd3VeSdBCCCHMgkqlMtlWGytWrGDy5MlMnDiRwMBA1qxZg729PevWrav2mPLycsaPH8+iRYvw9/e/q3glQQshhDALpkzQxcXF5OTkGG3FxcW3nbOkpISjR48yfPhwQ5larWb48OEcPHiw2r4uXryYpk2bMmnSpLuOVxK0EEIIxYmIiMDZ2dloi4iIuK2eVqulvLwcT09Po3JPT09SUlKqbPvnn3/m448/Zu3atX+qj7KKWwghhFkw5Sru8PBwwsLCjMpsbGz+dLu5ubk8+eSTrF27Fo1G86fakgQthBDCLJgyQdvY2NQoIWs0GiwsLLh586ZR+c2bN2nWrNlt9S9cuMDly5d56KGHDGU6nQ4AS0tLzp49S0BAQI36KFPcQgghRDWsra3p3r07UVFRhjKdTkdUVBR9+vS5rX779u1JSEggLi7OsI0cOZIhQ4YQFxeHj49Pjc8tI2ghhBDmoYGeUxIWFsaECRPo0aMHvXr1YuXKleTn5zNx4kQAQkND8fb2JiIiAltbWzp16mR0vIuLC8Bt5X9EErQQQgiz0FBPEhs3bhxpaWnMnz+flJQUgoOD2bt3r2HhWFJSEmq16SekJUELIYQQf2DatGlMmzatyn379u2747EbNmy4q3NKghZCCGEWlPYsbknQQgghzIIkaCGEEKIxUlZ+lq9ZCSGEEI2RjKCFEEKYBZniFkIIIRohSdBm5njUV8Tu3UlBdgYaH38GjX+OZv7tq6x7Yv9uzhz4nvTkKwA09W1Nn0cmGtXX6/VE79rEif/bS3FBHs1bBzIkdDount6GOkV5OezfupqLcdGoVCpad+/PwMefxdrWrm6DvWXb1k/YuP5jtNo02rZrz5xX5tE5KKja+t9+s4fI997henIyLX39eCHsRQYMHGTYr9frWb3qXT7fuYPc3ByCu3bj1fkL8fX1M9TJzsri368vYf++H1Gr1Qz72z3MnvMq9g4OdRmqEaXG/cyjA5k5YRie7k4knEsm7I0dHDl5pcq6TzwUwtrFTxqVFRWX4tp7plHZvGcfYOLovrg42nHw+EWmv76dC0lphv2uTvasmP137h/YCZ1ez66oOF5ctpP8whLTB1gFpb7Wj3RrzhMhPrg5WHM+NY/l353n1I3cKusObqthQp+WtHC1w1Kt4mpmIVtjrrL3ZOVvFD/d35fhHZri6WhDqU7H2ZQ81uy/xMnftPnmIx1p07QJrg7W5BaVcvhyFpH7LqLNq5/XWlTPrO9Bn4vZx0/bPyRk5Hj+sSASjY8/X654lYKcrCrrJ5+Np23IEMa8vIy/v/o2Tdw82LX8FfIytYY6R/d8Rtz3XzIk9HnGzX0HSxtbdi1/hbLSyjfrNx++QXryFUbPimDkjMUkn0vgh40r6zjaCnv37OatZRE889xUtu34gnbt2vPsM5NIT0+vsn7csVjmvDSL0WPGsn3nLoYMHcYLz08lMfGcoc76j9fy6SebmbtgIVs+/Qw7OzuenTLJ6KfXwme/yIXz51nz0XrejVxD7JEjLF44v87j/ZVS4x57TzfemDWapR/soc/jbxB/LpmvVk/Fw7VJtcdk5xbiNzzcsLW737i/s54aznOPDWL669sYGPoW+YUl/DdyKjbWldfr61+fQIcALx58dhWPTF9D/26tiZz3eJ3F+VtKfa2Ht/dgxtAAPvr5MhPWHyUxNY+V4zrjam9VZf2colI2HLzC5M3HeGLdEf6XkMLcB9oT0srVUCcpo5Dl3yYy/uMjPLMljhvZRbwzLggXu8o2jyZl8eqXpxj3YQzhX5zC28WW10cF1nm8d6Ohfg+6oZh1gj72zed0GngvgQNG4O7ty9DQ6Vha23Dqp2+qrD9iyhyChj6ER8sA3LxaMmziTPR6PVdPHQMqrrLjvttFr4ceI6BrXzQ+/tzz9MvkZ6VzMfYAABnXk7hy4gjDnppJs4D2NG/biUHjn+NczH7yMqv+ADGlzRvXM2bso4wa/QgBrVszd8EibG1t2fX5f6qs/8mWTfTtP4Cn/vk0/gEBTJv+Ah0CA9m2dYsh5k82b2LyM88yZOhw2rZrz2sRy0hLTeWHqO8BuHjhAr/8/BMLFr9GUFAXunXvwZxX5rJ3z9ekpt6s8rwSt2lMf2Io6z8/wOavDnHmYgrPL91GYVEJE0bd/gzgX+nRczM917ClZhiPwKY+PoQ31n7D//YlcCLxOk/P24SXhzMjh3QBoF0rT0b068hzi7dy+MQVDsRdJOyNHfx9RDe8PJzrNF5Q7mv9WK8WfHn8Bl8n3ORyegFv7E2kqFTHg0G3/yADQGxSNvvPpXM5vYDkrCI+O5LMhdQ8urSofI2+PZXK4StZXM8u4pK2gJVRF2hia0nrppWzAtsOJ3Pyei4pOcUkJOew+dBVOnk7YaFufElMEnQt6fV69Hq9KfpSK+VlpaReScQnsJuhTKVW4xPYlRsXTtWojbLiYnTlZdg6OAKQk5ZCQXaGUZs29g54+rfnxoXTANy4cBob+yZ4tmprqNMysBsqlYqbF8+YIrRqlZaUcPrUSXr36WsoU6vV9O7dl/jjx6o8Jj4ujt69jT/M+/brT3xcHADJ166h1aYR0ruyTUdHRzoHdTG0efz4MRydnOjYqbOhTkifvqjVahLi400VXrWUGreVpQVdO/jwQ/RZQ5ler+eH6LP0CmpV7XFN7Gw4u3sxiXuW8NnbU+jgX/kB7+ftjpeHMz9EV75Xc/KKOHziMiFBfgCEBLUiM6eA2FNJhjo/RJ9Fp9PTs5OvCSO8nVJfa0u1inbNHDl8OdNQpgcOX86ks7dTjdro4etCSzd74q5mV3uOUcFe5BaVkZiaV2UdJ1tLRnRsSsK1HMp19f+5Lozd9T3ojz/+mLfffpvExEQA2rRpwwsvvMDTTz/9h8cWFxcbTS3djcLcHPQ6HfZOLkbl9k6uZN64WqM2ftn5MQ4u7vh0rEjIBTkZt9r4fZsuFGRX7CvIzsDO0Xi/2sICWwdH8m8dX1cyszIpLy/H3d3dqNzd3Z1Lly5WeYxWq8XdXXNbfW269tb+ivuO7prb29RqK+qka7W4ubkZ7be0tMTJ2Zl0bRp1Talxa1ybYGlpcdsIODU9h3Z+nlUek3gllWcWfcKJc8k4OdrxwpPD+HHDLLqPXUpyahbNNBUf9re3mYune8U+T3cn0n63v7xcR0ZOAZ6amiWLu6XU19rF3gpLtYqM/FKj8sz8Uvzc7as9zsHGgv9O7YO1hYpyPbz5bSIxv0nyAP0C3FjycCC2Vmq0eSVM3xZPdmGZUZ2pg1sxtps3dtYWJCTnMGtHgumCMyXzGPiazF0l6Pnz57NixQqef/55w89tHTx4kJkzZ5KUlMTixYvveHxERASLFi26m1ObzJGvt3MuZh+PvPwmllbWDdoXIUwlOv4S0fGXDP8+dPwicf+Zx6Sx/Vi8+usG7JmoCwXF5YSuO4KdtQU9/VyZMTSA61mFxCZVjqKPJmURuu4IzvZWPNzFi6WjOjBp0zEyCyovBrZEX+Wr4yl4OdsyqZ8vCx5sz6ydJxoipDsyl6lpU7mrKe7333+ftWvXEhERwciRIxk5ciQRERF8+OGHrF69+g+PDw8PJzs722irLTtHJ1Rq9W0LwgpyMrF3dq36oFti9+7gyO7tjAqLQOPjbyi3d3K71cbv28zC3rlin72zG4W5xvt15eUU5efi4GR8BW5qri6uWFhY3LZYJj09HY1GU+UxGo2G9HTt7fVvjTg0Go+KMm31bbprNGRkGM8OlJWVkZOdjfut4+uSUuPWZuZRVlZOUzdHo/Km7k6kpOfUqI2yMh3Hz14lwKeivynaiuNub9ORm7favJmeg8fv9ltYqHFzsuemtmbnvVtKfa2zCkop0+lxczBeEObqYEV6fvWrqfXAtawiElPz2RpzjR/PphHau6VRnaJSHdeyijh5PZfX95yjXKfnod/d184uLONqZiExlzOZ+9Up+rV2p1Pzup0tEX/srhJ0aWkpPXr0uK28e/fulJWVVXGEMRsbG5ycnIy22rKwtKKpbxuunq68L6XX6bh6Og6vgOpXIB7d8xkx/93Kw2FLje4jAzh5NMPe2c2waAyguDCfmxfP4BXQAQCvgA4UF+SRejnRUOfq6Tj0ej2e1Xy9y1SsrK3pENiR6EMHDWU6nY7o6IMEdela5TFBwcFEHzpkVHbo4AGCgoMB8G7RAo3Gg+joyjbz8vJIiD9uaLNLl67k5uRw6mTlFXVM9CF0Ot0dv/piKkqNu7SsnGOnrzIkpJ2hTKVSMaRXW2J+M0q+E7VaRcfWzQ2J+XJyOjfSso3adHSwpWcnP6LjLwMVo3BXJ3u6dqj8YfnBPduiVqs4fKLqr3eZilJf6zKdnrMpufT0qxxcqICevq4kJNf8okilAmvLO3+sq1SqO9ZR3xqlWls2vtGqLBKrgSeffJL333//tvIPP/yQ8ePH/+lO1VTXEWM4uX8Pp3/5jozrSfy4+T3KiosI7H8PAN+uXcYvO9cZ6h/ZvZ2DX2xi+MQwnDSe5GdnkJ+dQUlRIVDx4gf/bRSH//cpF48dRHvtEt999CYOLu74d6tYYOLWvCW+nXoQtWElKRfPcD3xJPs/iaRtr0E0cXW/vZMm9uSEiXy+8zO+2vUFFy9c4LXFCyksLGTU6DEAvBr+Mu+8vdxQf/wToRz45Sc2bljHpYsXeD/yPU6eOME/Hn/CEPP4J0NZ+8H77PshisRzZ5kb/jIeTZsydNhwAPwDAujXfwCLFswjIT6eY7FHiVi6hHvve4CmTau+Fypxm8a7W35g4ui+jH8ohHatPHn3lXHY29mw6cuKhPTRkidZ/PxIQ/3wKfcyrHd7/LzdCW7fgvVLJ9DSy431Xxww1Inc+iOzn76XBwZ1pmPr5ny85ElupGXz1Y/HATh76Sbf/HKSyHmP06OjL326+PP2nEfZ8U0sN9JqP9tVW0p9rT+NucbILl7c38kTP3d7Xh7RBltrNV/HpwAw/8F2PDuocnFgaG8fevm50tzZFj93ex7v1YL7Onqy90TFqnNbKzX/GtiKjs0daeZkQzvPJrx6f1s8HG2IOlNxX72jlyNjuzWnTVMHmjnZ0N3XhSUjO3A1s7BWFwb1RaUy3WYOanwPOiwszPDfKpWKjz76iG+//ZbevXsDEB0dTVJSEqGhoabvZTXa9hpMYW42h3ZtIj87Ew8ffx6eudQwxZ2bkYbqNz+infDj1+jKStm9+jWjdnqNfILeoyoe7tD9vkcpKy7ih43vVDyopE1HHg5banSfesSU2ez7JJIv3pyDSv3rg0qeq4eI4d777iczI4PVq95Fq02jXfsOrP7gI9xvTdWl3LiBWlUZc3DXbkQse4tV767kvZUraOnrx8r3ImnTpnL2YOKkyRQWFrJ44Xxyc3Po2q07qz/4CBsbG0OdiDfeImLpEqZMmmB4iMOc8Ln1ErOS4975bSwa1ybMf/YBPN0diT+bzMNTIw2LvHyauaH7zWpbV0d7Vs9/HE93RzJzCjl2OokhT63gzMUUQ53lG77H3s6GVXMfw8XRjgNxFxg5dTXFJZWzXxNf2cjbcx5l9wfPo9NVPKhk1rId9RKzUl/r78+k4WJvxeQBfrg7WJOYmsfM7Qlk3LpX3MzJlt9+YcbOyoKX7mmNh6MNxWU6rqQXsPC/Z/j+VvLV6fT4udtxf+eOuNhZkV1YyumUXP61JY5L2gIAisp0DG6nYfIAP2ytLEjPK+bQxUzWHzhFaXnjW8VtLiNfU1Hpa/gdqSFDhtSsQZWKH374ofYdUalY9XPNpu3+Cqb1r7gSLixtfH8EdcnOquIPTKlx2wZPbeCe1J+iuEhAua91SMS+hu1IPYoOH1wvX7dt89Jek7WV+Oa9JmurrtR4BP3jjz/WZT+EEEKIO1LYANr8n8UthBBCGZQ2xW3Wj/oUQggh/qpkBC2EEMIsKGwALQlaCCGEeVA3wh/wqEsyxS2EEEI0QjKCFkIIYRZkilsIIYRohGQVtxBCCCEanIyghRBCmAWFDaAlQQshhDAPSpvilgQthBDCLCgtQcs9aCGEEKIRkhG0EEIIs6CwAbQkaCGEEOZBpriFEEII0eBkBC2EEMIsKGwALQlaCCGEeZApbiGEEEI0OBlBCyGEMAsKG0BLghZCCGEeZIpbCCGEEA1ORtBCCCHMgsIG0JKghRBCmAelTXGr9Hq9vqE7Acr7P14IIf5K6iOV9P73fpO1dWjOIJO1VVfkHrQQQgjRCDWqKe5VP19q6C7Um2n9WwFQWNooJjDqjZ1VxUyJxP3Xp8SYoTLukIh9DduRehQdPrhezqO0mdZGlaCFEEKI6igsP8sUtxBCCNEYyQhaCCGEWZApbiGEEKIRUlh+liluIYQQojGSEbQQQgizIFPcQgghRCOktAQtU9xCCCFEIyQjaCGEEGZBYQNoSdBCCCHMg9KmuCVBCyGEMAsKy89yD1oIIYRojGQELYQQwizIFLcQQgjRCCksP8sUtxBCCNEYyQhaCCGEWVArbAgtCVoIIYRZUFh+liluIYQQojGSEbQQQgizoLRV3DKCFkIIYRbUKtNttRUZGYmfnx+2traEhIQQExNTbd3PP/+cHj164OLigoODA8HBwWzevLn28da+m0IIIUT9U6lUJttqY/v27YSFhbFgwQJiY2Pp0qULI0aMIDU1tcr6bm5uvPrqqxw8eJD4+HgmTpzIxIkT+eabb2p1XknQQgghxB2sWLGCyZMnM3HiRAIDA1mzZg329vasW7euyvqDBw9m9OjRdOjQgYCAAGbMmEFQUBA///xzrc4rCVoIIYRZUKlMtxUXF5OTk2O0FRcX33bOkpISjh49yvDhww1larWa4cOHc/DgwT/ss16vJyoqirNnzzJw4MBaxWv2i8SOR31F7N6dFGRnoPHxZ9D452jm377Kuif27+bMge9JT74CQFPf1vR5ZKJRfb1eT/SuTZz4v70UF+TRvHUgQ0Kn4+LpbahTlJfD/q2ruRgXjUqlonX3/gx8/Fmsbe3qNthbtm39hI3rP0arTaNtu/bMeWUenYOCqq3/7Td7iHzvHa4nJ9PS148Xwl5kwMBBhv16vZ7Vq97l8507yM3NIbhrN16dvxBfXz9DneysLP79+hL27/sRtVrNsL/dw+w5r2Lv4FCXoRqRuJUTtxJjBnikW3OeCPHBzcGa86l5LP/uPKdu5FZZd3BbDRP6tKSFqx2WahVXMwvZGnOVvScrp12f7u/L8A5N8XS0oVSn42xKHmv2X+Lkb9p885GOtGnaBFcHa3KLSjl8OYvIfRfR5pXUeby1pcJ0i8QiIiJYtGiRUdmCBQtYuHChUZlWq6W8vBxPT0+jck9PT86cOVNt+9nZ2Xh7e1NcXIyFhQWrV6/mb3/7W636aNYj6HMx+/hp+4eEjBzPPxZEovHx58sVr1KQk1Vl/eSz8bQNGcKYl5fx91ffpombB7uWv0JeptZQ5+iez4j7/kuGhD7PuLnvYGljy67lr1BWWvlm/ebDN0hPvsLoWRGMnLGY5HMJ/LBxZR1HW2Hvnt28tSyCZ56byrYdX9CuXXuefWYS6enpVdaPOxbLnJdmMXrMWLbv3MWQocN44fmpJCaeM9RZ//FaPv1kM3MXLGTLp59hZ2fHs1MmGV1Nhs9+kQvnz7Pmo/W8G7mG2CNHWLxwfp3H+yuJWzlxKzFmgOHtPZgxNICPfr7MhPVHSUzNY+W4zrjaW1VZP6eolA0HrzB58zGeWHeE/yWkMPeB9oS0cjXUScooZPm3iYz/+AjPbInjRnYR74wLwsWuss2jSVm8+uUpxn0YQ/gXp/B2seX1UYF1Hm9DCw8PJzs722gLDw83WfuOjo7ExcVx+PBhli5dSlhYGPv27atVG2adoI998zmdBt5L4IARuHv7MjR0OpbWNpz6qeob8SOmzCFo6EN4tAzAzaslwybORK/Xc/XUMaDiKjvuu130eugxArr2RePjzz1Pv0x+VjoXYw8AkHE9iSsnjjDsqZk0C2hP87adGDT+Oc7F7Ccvs+oPEFPavHE9Y8Y+yqjRjxDQujVzFyzC1taWXZ//p8r6n2zZRN/+A3jqn0/jHxDAtOkv0CEwkG1btxhi/mTzJiY/8yxDhg6nbbv2vBaxjLTUVH6I+h6Aixcu8MvPP7Fg8WsEBXWhW/cezHllLnv3fE1q6s06j1niVlbcSowZ4LFeLfjy+A2+TrjJ5fQC3tibSFGpjgeDmlVZPzYpm/3n0rmcXkByVhGfHUnmQmoeXVo4G+p8eyqVw1eyuJ5dxCVtASujLtDE1pLWTStnBbYdTubk9VxScopJSM5h86GrdPJ2wuJuljrXMVOu4raxscHJyclos7Gxue2cGo0GCwsLbt40fh/cvHmTZs2qfm2gYhq8devWBAcHM2vWLMaOHUtERETt4q1V7UakvKyU1CuJ+AR2M5Sp1Gp8Arty48KpGrVRVlyMrrwMWwdHAHLSUijIzjBq08beAU//9ty4cBqAGxdOY2PfBM9WbQ11WgZ2Q6VScfNi9dMdplBaUsLpUyfp3aevoUytVtO7d1/ijx+r8pj4uDh69+5jVNa3X3/i4+IASL52Da02jZDelW06OjrSOaiLoc3jx4/h6OREx06dDXVC+vRFrVaTEB9vqvCqJXErJ24lxgxgqVbRrpkjhy9nGsr0wOHLmXT2dqpRGz18XWjpZk/c1exqzzEq2IvcojISU/OqrONka8mIjk1JuJZDuU5f6zjqWkOs4ra2tqZ79+5ERUUZynQ6HVFRUfTp0+cORxrT6XRV3uO+k7u6Bx0REYGnpyf//Oc/jcrXrVtHWloas2fPvptma6UwNwe9Toe9k4tRub2TK5k3rtaojV92foyDizs+HSsSckFOxq02ft+mCwXZFfsKsjOwczTer7awwNbBkfxbx9eVzKxMysvLcXd3Nyp3d3fn0qWLVR6j1Wpxd9fcVl+brr21P62iTHN7m1ptRZ10rRY3Nzej/ZaWljg5O5N+6/i6JHErJ24lxgzgYm+FpVpFRn6pUXlmfil+7vbVHudgY8F/p/bB2kJFuR7e/DaRmN8keYB+AW4seTgQWys12rwSpm+LJ7uwzKjO1MGtGNvNGztrCxKSc5i1I8F0wf0FhIWFMWHCBHr06EGvXr1YuXIl+fn5TJw4EYDQ0FC8vb0NI+SIiAh69OhBQEAAxcXF7N69m82bN/P+++/X6rx3laA/+OADtm7delt5x44d+cc//vGHCbq4uLjWVxKmduTr7ZyL2ccjL7+JpZV1g/ZFCCHuRkFxOaHrjmBnbUFPP1dmDA3gelYhsUmVo+ijSVmErjuCs70VD3fxYumoDkzadIzMgsqLgS3RV/nqeApezrZM6ufLggfbM2vniYYI6Y4a6kFi48aNIy0tjfnz55OSkkJwcDB79+41LBxLSkpCra6ckM7Pz+e5557j2rVr2NnZ0b59e7Zs2cK4ceNqdd67muJOSUnBy8vrtnIPDw9u3Ljxh8dHRETg7OxstNWWnaMTKrX6tgVhBTmZ2Du7Vn3QLbF7d3Bk93ZGhUWg8fE3lNs7ud1q4/dtZmHvXLHP3tmNwlzj/brycoryc3FwMr4CNzVXF1csLCxuWyyTnp6ORqOp8hiNRkN6uvb2+rdGHBqNR0WZtvo23TUaMjKMZwfKysrIyc7G/dbxdUniVk7cSowZIKuglDKdHjcH4wVhrg5WpOdXv5paD1zLKiIxNZ+tMdf48Wwaob1bGtUpKtVxLauIk9dzeX3POcp1eh763X3t7MIyrmYWEnM5k7lfnaJfa3c6Na/Z1Hp9UqtUJttqa9q0aVy5coXi4mKio6MJCQkx7Nu3bx8bNmww/Pu1114jMTGRwsJCMjIyOHDgQK2TM9xlgvbx8eGXX365rfyXX36hefPmf3h8VavnasvC0oqmvm24erryvpRep+Pq6Ti8AqpfgXh0z2fE/HcrD4ctNbqPDODk0Qx7ZzfDojGA4sJ8bl48g1dABwC8AjpQXJBH6uVEQ52rp+PQ6/V4VvP1LlOxsramQ2BHog9VfvdOp9MRHX2QoC5dqzwmKDiY6EOHjMoOHTxAUHAwAN4tWqDReBAdXdlmXl4eCfHHDW126dKV3JwcTp2svKKOiT6ETqe741dfTEXiVk7cSowZoEyn52xKLj39KgcXKqCnrysJyTk1bkelAmvLO3+sq1SqO9b5NXlZWza+RWJKc1dT3JMnT+aFF16gtLSUoUOHAhAVFcXLL7/MrFmz/vB4GxubKlfL1VbXEWP47qO38PRri2erdsR99wVlxUUE9r8HgG/XLsPBVUO/sRX3yo/s3s6hXZu5d8psnDSe5N+6r2xlY4e1rR0qlYrgv43i8P8+xcXTGyePZhz6YiMOLu74d6tYYOLWvCW+nXoQtWElQ0KfR1dezv5PImnbaxBNXN2r7qgJPTlhIvNemU3Hjp3o1DmILZs3UlhYyKjRYwB4Nfxlmjb1ZMbMitdh/BOhTHrqSTZuWMfAgYPYu2c3J0+cYN7CxUDFH+v4J0NZ+8H7+Lb0xbtFCyLfewePpk0ZOqzii/n+AQH06z+ARQvmMXf+IsrKSolYuoR773uApk09q+6oxC1xS8y18mnMNeY92J7TN3I5dSOXcT28sbVW83V8CgDzH2xHWm4J7++/BEBobx/OpORxLbMQa0s1fQPcuK+jJ8u+qRg82FqpeaqPLz+d15KeV4KznRVjuzfHw9GGqDMV99U7ejnSwcuR49eyyS0qw9vVjmcG+HE1s7BWFwb1RWG/lXF3Cfqll14iPT2d5557jpKSiukXW1tbZs+ebdLvkf2Rtr0GU5ibzaFdm8jPzsTDx5+HZy41THHnZqSh+s19gYQfv0ZXVsru1a8ZtdNr5BP0HvUkAN3ve5Sy4iJ+2PhOxYNK2nTk4bClRvepR0yZzb5PIvnizTmo1L8+qOS5eogY7r3vfjIzMli96l202jTate/A6g8+wv3WVF3KjRuoVZUxB3ftRsSyt1j17kreW7mClr5+rHwvkjZtKmcPJk6aTGFhIYsXzic3N4eu3bqz+oOPjC6iIt54i4ilS5gyaYLhIQ5zwufWS8wSt7LiVmLMAN+fScPF3orJA/xwd7AmMTWPmdsTyLh1r7iZky363yystrOy4KV7WuPhaENxmY4r6QUs/O8Zvr+VfHU6PX7udtzfuSMudlZkF5ZyOiWXf22J45K2AICiMh2D22mYPMAPWysL0vOKOXQxk/UHTlFa3jhXcSuJSq/X3/WrkJeXx+nTp7Gzs6NNmzZ/alSsUqlY9fOluz7e3Ezr3wqAwtLG90dQl+ysKv7AJO6/PiXGDJVxh0Tsa9iO1KPo8MH8iVRSY3/fEGuytnY81e2PKzWwP/WozyZNmtCzZ09T9UUIIYQQt5j9s7iFEEIow92svjZnkqCFEEKYBWWlZzN+1KcQQgjxVyYjaCGEEGZBaau4JUELIYQwC43wB7bqlExxCyGEEI2QjKCFEEKYBZniFkIIIRohheVnmeIWQgghGiMZQQshhDALMsUthBBCNEJKW8UtCVoIIYRZUNoIWu5BCyGEEI2QjKCFEEKYBWWNnyVBCyGEMBNK+zUrmeIWQgghGiEZQQshhDALChtAS4IWQghhHmQVtxBCCCEanIyghRBCmAWFDaAlQQshhDAPsopbCCGEEA1ORtBCCCHMgsIG0Kj0er2+oTsByludJ4QQfyX1kUqmfnHaZG1Fju5gsrbqioyghRBCmAWl3ZNtVAl61c+XGroL9WZa/1YA2AZPbeCe1K+iuEgAQiL2NWxH6ll0+GAACksbxYRVvbCzqpgVU1LMoMy4f41ZmFajStBCCCFEdZR2K1QStBBCCLOgVlZ+VtyUvhBCCGEWZAQthBDCLChtBC0JWgghhFlQ2j1omeIWQgghGiEZQQshhDALMsUthBBCNEIKm+GWKW4hhBCiMZIRtBBCCLOgtJ+blAQthBDCLChtylcStBBCCLOgsAG04i5IhBBCCLMgI2ghhBBmQe5BCyGEEI2QwvKzTHELIYQQjZGMoIUQQpgFeZKYEEII0Qgp7R60THELIYQQjZCMoIUQQpgFhQ2gJUELIYQwD0q7By1T3EIIIUQjJCNoIYQQZkGFsobQkqCFEEKYBaVNcZt9gj4e9RWxe3dSkJ2BxsefQeOfo5l/+yrrnti/mzMHvic9+QoATX1b0+eRiUb19Xo90bs2ceL/9lJckEfz1oEMCZ2Oi6e3oU5RXg77t67mYlw0KpWK1t37M/DxZ7G2tavbYG955tGBzJwwDE93JxLOJRP2xg6OnLxSZd0nHgph7eInjcqKiktx7T3TqGzesw8wcXRfXBztOHj8ItNf386FpDTDflcne1bM/jv3D+yETq9nV1QcLy7bSX5hiekDrMYj3ZrzRIgPbg7WnE/NY/l35zl1I7fKuoPbapjQpyUtXO2wVKu4mlnI1pir7D2ZaqjzdH9fhndoiqejDaU6HWdT8liz/xInf9Pmm490pE3TJrg6WJNbVMrhy1lE7ruINq/+4t629RM2rv8YrTaNtu3aM+eVeXQOCqq2/rff7CHyvXe4npxMS18/Xgh7kQEDBxn26/V6Vq96l8937iA3N4fgrt14df5CfH39DHWys7L49+tL2L/vR9RqNcP+dg+z57yKvYNDXYZqoMSYQblx15TSErRZ34M+F7OPn7Z/SMjI8fxjQSQaH3++XPEqBTlZVdZPPhtP25AhjHl5GX9/9W2auHmwa/kr5GVqDXWO7vmMuO+/ZEjo84yb+w6WNrbsWv4KZaWVH8jffPgG6clXGD0rgpEzFpN8LoEfNq6s42grjL2nG2/MGs3SD/bQ5/E3iD+XzFerp+Lh2qTaY7JzC/EbHm7Y2t0/32j/rKeG89xjg5j++jYGhr5FfmEJ/42cio115fXb+tcn0CHAiwefXcUj09fQv1trIuc9Xmdx/t7w9h7MGBrARz9fZsL6oySm5rFyXGdc7a2qrJ9TVMqGg1eYvPkYT6w7wv8SUpj7QHtCWrka6iRlFLL820TGf3yEZ7bEcSO7iHfGBeFiV9nm0aQsXv3yFOM+jCH8i1N4u9jy+qjAOo/3V3v37OatZRE889xUtu34gnbt2vPsM5NIT0+vsn7csVjmvDSL0WPGsn3nLoYMHcYLz08lMfGcoc76j9fy6SebmbtgIVs+/Qw7OzuenTKJ4uJiQ53w2S9y4fx51ny0nncj1xB75AiLF86v6pQmp8SYQblxi+qZdYI+9s3ndBp4L4EDRuDu7cvQ0OlYWttw6qdvqqw/YsocgoY+hEfLANy8WjJs4kz0ej1XTx0DKq42477bRa+HHiOga180Pv7c8/TL5GelczH2AAAZ15O4cuIIw56aSbOA9jRv24lB45/jXMx+8jKr/kMypelPDGX95wfY/NUhzlxM4fml2ygsKmHCqD7VHqNHz830XMOWmmE86pz6+BDeWPsN/9uXwInE6zw9bxNeHs6MHNIFgHatPBnRryPPLd7K4RNXOBB3kbA3dvD3Ed3w8nCu03h/9VivFnx5/AZfJ9zkcnoBb+xNpKhUx4NBzaqsH5uUzf5z6VxOLyA5q4jPjiRzITWPLi0q+/vtqVQOX8nienYRl7QFrIy6QBNbS1o3rRw5bDuczMnruaTkFJOQnMPmQ1fp5O2ERT1dym/euJ4xYx9l1OhHCGjdmrkLFmFra8uuz/9TZf1Ptmyib/8BPPXPp/EPCGDa9BfoEBjItq1bgIr3+CebNzH5mWcZMnQ4bdu157WIZaSlpvJD1PcAXLxwgV9+/okFi18jKKgL3br3YM4rc9m752tSU29KzBJ3g1GpVCbbzIHZJujyslJSryTiE9jNUKZSq/EJ7MqNC6dq1EZZcTG68jJsHRwByElLoSA7w6hNG3sHPP3bc+PCaQBuXDiNjX0TPFu1NdRpGdgNlUrFzYtnTBFatawsLejawYcfos8ayvR6PT9En6VXUKtqj2tiZ8PZ3YtJ3LOEz96eQgf/yqTm5+2Ol4czP0RX9j0nr4jDJy4TEuQHQEhQKzJzCog9lWSo80P0WXQ6PT07+ZowwqpZqlW0a+bI4cuZhjI9cPhyJp29nWrURg9fF1q62RN3Nbvac4wK9iK3qIzE1Lwq6zjZWjKiY1MSruVQrtPXOo7aKi0p4fSpk/Tu09dQplar6d27L/HHj1V5THxcHL17G1+s9e3Xn/i4OACSr11Dq00jpHdlm46OjnQO6mJo8/jxYzg6OdGxU2dDnZA+fVGr1STEx5sqvCopMWZQbty1pVaZbjMHNb4HHRYWVuNGV6xYccf9xcXFRlMsd6MwNwe9Toe9k4tRub2TK5k3rtaojV92foyDizs+HSsSckFOxq02ft+mCwXZFfsKsjOwczTer7awwNbBkfxbx9cVjWsTLC0tbhsBp6bn0M7Ps8pjEq+k8syiTzhxLhknRzteeHIYP26YRfexS0lOzaKZpiLB3d5mLp7uFfs83Z1I+93+8nIdGTkFeGpqliD/DBd7KyzVKjLyS43KM/NL8XO3r/Y4BxsL/ju1D9YWKsr18Oa3icT8JskD9AtwY8nDgdhaqdHmlTB9WzzZhWVGdaYObsXYbt7YWVuQkJzDrB0JpgvuDjKzMikvL8fd3d2o3N3dnUuXLlZ5jFarxd1dc1t9bbr21v6KdQXumtvb1Gor6qRrtbi5uRntt7S0xMnZmXRtGnVJiTGDcuMWd1bjBH3smPFVXGxsLGVlZbRr1w6Ac+fOYWFhQffu3f+wrYiICBYtWlTLrprWka+3cy5mH4+8/CaWVtYN2pe6FB1/iej4S4Z/Hzp+kbj/zGPS2H4sXv11A/as7hUUlxO67gh21hb09HNlxtAArmcVEptUOYo+mpRF6LojONtb8XAXL5aO6sCkTcfILKi8GNgSfZWvjqfg5WzLpH6+LHiwPbN2nmiIkIRQNDOZmTaZGk9x//jjj4btoYceYtCgQVy7do3Y2FhiY2O5evUqQ4YM4YEHHvjDtsLDw8nOzjbaasvO0QmVWn3bgrCCnEzsnV2rPuiW2L07OLJ7O6PCItD4+BvK7Z3cbrXx+zazsHeu2Gfv7EZhrvF+XXk5Rfm5ODgZX4mamjYzj7Kycpq6ORqVN3V3IiU9p0ZtlJXpOH72KgE+HgCkaCuOu71NR27eavNmeg4ev9tvYaHGzcmem9qanffPyCoopUynx83BeEGYq4MV6fnVr6bWA9eyikhMzWdrzDV+PJtGaO+WRnWKSnVcyyri5PVcXt9zjnKdnod+d187u7CMq5mFxFzOZO5Xp+jX2p1Ozet+5sDVxRULC4vbFgmlp6ej0WiqPEaj0ZCerr29/q2RlkZT8bqna6tv012jISPDeDaorKyMnOxs3G8dX1eUGDMoN+7aUqtUJtvMwV3dg16+fDkRERG4ulYmQldXV1577TWWL1/+h8fb2Njg5ORktNWWhaUVTX3bcPV05cher9Nx9XQcXgHVr7I9uuczYv67lYfDlhrdRwZw8miGvbObYdEYQHFhPjcvnsEroAMAXgEdKC7II/VyoqHO1dNx6PV6PKv5epeplJaVc+z0VYaEtDOUqVQqhvRqS8xvRsl3olar6Ni6uSExX05O50ZatlGbjg629OzkR3T8ZaBiFO7qZE/XDj6GOoN7tkWtVnH4RNVf7zKlMp2esym59PSrfL+pgJ6+riQk1/wCQaUCa8s7v+VVKtUd6/z6h21tWfd/4FbW1nQI7Ej0oYOGMp1OR3T0QYK6dK3ymKDgYKIPHTIqO3TwAEHBwQB4t2iBRuNBdHRlm3l5eSTEHze02aVLV3Jzcjh1snKWICb6EDqd7o5f+TEFJcYMyo1b3NldJeicnBzS0m6/P5GWlkZubtXfS60LXUeM4eT+PZz+5Tsyrifx4+b3KCsuIrD/PQB8u3YZv+xcZ6h/ZPd2Dn6xieETw3DSeJKfnUF+dgYlRYVAxYdz8N9Gcfh/n3Lx2EG01y7x3Udv4uDijn+3ioUWbs1b4tupB1EbVpJy8QzXE0+y/5NI2vYaRBNX99s7aWLvbvmBiaP7Mv6hENq18uTdV8Zhb2fDpi8r/lA/WvIki58faagfPuVehvVuj5+3O8HtW7B+6QRaermx/osDhjqRW39k9tP38sCgznRs3ZyPlzzJjbRsvvrxOABnL93km19OEjnvcXp09KVPF3/envMoO76J5UZa7Wc/7sanMdcY2cWL+zt54uduz8sj2mBrrebr+BQA5j/YjmcHVS6UC+3tQy8/V5o72+Lnbs/jvVpwX0dP9p6oWJlqa6XmXwNb0bG5I82cbGjn2YRX72+Lh6MNUWcq3tsdvRwZ2605bZo60MzJhu6+LiwZ2YGrmYW1ujD4M56cMJHPd37GV7u+4OKFC7y2eCGFhYWMGj0GgFfDX+adtysvisc/EcqBX35i44Z1XLp4gfcj3+PkiRP84/EngIr3+PgnQ1n7wfvs+yGKxHNnmRv+Mh5NmzJ02HAA/AMC6Nd/AIsWzCMhPp5jsUeJWLqEe+97gKZNq17rIDFL3PWhIReJRUZG4ufnh62tLSEhIcTExFRbd+3atQwYMABXV1dcXV0ZPnz4HetX564eVDJ69GgmTpzI8uXL6dWrFwDR0dG89NJLjBkz5m6avCttew2mMDebQ7s2kZ+diYePPw/PXGqY4s7NSEOlrrwGSfjxa3Rlpexe/ZpRO71GPkHvURUP8+h+36OUFRfxw8Z3Kh5U0qYjD4ctNbpPPWLKbPZ9EskXb85Bpf71QSXP1UPEsPPbWDSuTZj/7AN4ujsSfzaZh6dGGhZ5+TRzQ/ebFcaujvasnv84nu6OZOYUcux0EkOeWsGZiymGOss3fI+9nQ2r5j6Gi6MdB+IuMHLqaopLKhdLTXxlI2/PeZTdHzyPTlfxoJJZy3bUS8wA359Jw8XeiskD/HB3sCYxNY+Z2xPIuHWvuJmTLfrfLKy2s7LgpXta4+FoQ3GZjivpBSz87xm+v5V8dTo9fu523N+5Iy52VmQXlnI6JZd/bYnjkrYAgKIyHYPbaZg8wA9bKwvS84o5dDGT9QdOUVpe96u4Ae69734yMzJYvepdtNo02rXvwOoPPsL91hRlyo0bqFWV7/Hgrt2IWPYWq95dyXsrV9DS14+V70XSpk3lbNHESZMpLCxk8cL55Obm0LVbd1Z/8BE2NjaGOhFvvEXE0iVMmTTB8PCKOeFzJWaJu0E11Mz09u3bCQsLY82aNYSEhLBy5UpGjBjB2bNnadq06W319+3bx2OPPUbfvn2xtbXljTfe4J577uHkyZN4e3tXcYaqqfR6fa0/aQoKCnjxxRdZt24dpaUVH5CWlpZMmjSJN998E4e7eAKNSqVi1c81m6b9K5jWv2K0Zxs8tYF7Ur+K4iIBCInY17AdqWfR4YMBKCytn8TeGNhZVXyaKilmUGbcdlYq7iKV1Np7v5guR0zp0fy2bxPZ2NgYXbz8KiQkhJ49e7Jq1Sqg4vaDj48Pzz//PHPmzPnDc5WXl+Pq6sqqVasIDQ2tcR/vaorb3t6e1atXk56ezrFjxzh27BgZGRmsXr36rpKzEEII8UfUqEy2RURE4OzsbLRFRETcds6SkhKOHj3K8OHDK/uhVjN8+HAOHjx4W/2qFBQUUFpaettX2v7In3oWt4ODA0GykEAIIUQ9MOUUd3h4+G3P96hq9KzVaikvL8fT0/ievKenJ2fO1OzhVLNnz6Z58+ZGSb4mzP7HMoQQQiiDKZ8AVt10tqn9+9//Ztu2bezbtw9bW9taHSsJWgghhKiGRqPBwsKCmzeNn01+8+ZNmjWr+rcAfvXWW2/x73//m++///6uZpvN9lncQgghlKUhHlRibW1N9+7diYqKMpTpdDqioqLo06f6HylatmwZS5YsYe/evfTo0eOu4pURtBBCCLPQUF+zCgsLY8KECfTo0YNevXqxcuVK8vPzmThxIgChoaF4e3sbFpm98cYbzJ8/n61bt+Ln50dKSsXXWps0aUKTJtX/NPDvSYIWQggh7mDcuHGkpaUxf/58UlJSCA4OZu/evYaFY0lJSah/88yN999/n5KSEsaOHWvUzoIFC1i4cGGNzysJWgghhFloyGdoT5s2jWnTplW5b9++fUb/vnz5sknOKQlaCCGEWTCT37gwGVkkJoQQQjRCMoIWQghhFpQ2opQELYQQwiyoFDbHrbQLEiGEEMIsyAhaCCGEWVDW+FkStBBCCDPRkF+zagiSoIUQQpgFZaVnuQcthBBCNEoyghZCCGEWFDbDLQlaCCGEeZCvWQkhhBCiwckIWgghhFlQ2ohSErQQQgizIFPcQgghhGhwMoIWQghhFpQ1fgaVXq/XN3QnQHlTF0II8VdSH6lk5/EbJmtrbBcvk7VVV2SKWwghhGiEGtUU96qfLzV0F+rNtP6tALANntrAPalfRXGRAIRE7GvYjtSz6PDBgLJe719f68LSRjFJV2/srCpmA5X0Hv/1/V3XlDaibFQJWgghhKiO0m6FSoIWQghhFpSVnpU3YyCEEEKYBRlBCyGEMAsKm+GWBC2EEMI8qBU2yS1T3EIIIUQjJCNoIYQQZkGmuIUQQohGSCVT3EIIIYRoaDKCFkIIYRZkilsIIYRohGQVtxBCCCEanIyghRBCmAWZ4hZCCCEaIUnQQgghRCMkX7MSQgghRIOTEbQQQgizoFbWAFoStBBCCPMgU9xCCCGEaHAyghZCCGEWZBW3EEII0QjJFLcQQgghGpyMoIUQQpgFWcUthBBCNEJKm+I2+wR9POorYvfupCA7A42PP4PGP0cz//ZV1j2xfzdnDnxPevIVAJr6tqbPIxON6uv1eqJ3beLE/+2luCCP5q0DGRI6HRdPb0Odorwc9m9dzcW4aFQqFa2792fg489ibWtXt8He8syjA5k5YRie7k4knEsm7I0dHDl5pcq6TzwUwtrFTxqVFRWX4tp7plHZvGcfYOLovrg42nHw+EWmv76dC0lphv2uTvasmP137h/YCZ1ez66oOF5ctpP8whLTB1iNR7o154kQH9wcrDmfmsfy785z6kZulXUHt9UwoU9LWrjaYalWcTWzkK0xV9l7MtVQ5+n+vgzv0BRPRxtKdTrOpuSxZv8lTv6mzTcf6Uibpk1wdbAmt6iUw5eziNx3EW1e/cWtxNd729ZP2Lj+Y7TaNNq2a8+cV+bROSio2vrffrOHyPfe4XpyMi19/Xgh7EUGDBxk2K/X61m96l0+37mD3Nwcgrt249X5C/H19TPUyc7K4t+vL2H/vh9Rq9UM+9s9zJ7zKvYODnUZqhGlvsdF1cz6HvS5mH38tP1DQkaO5x8LItH4+PPlilcpyMmqsn7y2XjahgxhzMvL+Purb9PEzYNdy18hL1NrqHN0z2fEff8lQ0KfZ9zcd7C0sWXX8lcoK618s37z4RukJ19h9KwIRs5YTPK5BH7YuLKOo60w9p5uvDFrNEs/2EOfx98g/lwyX62eiodrk2qPyc4txG94uGFrd/98o/2znhrOc48NYvrr2xgY+hb5hSX8N3IqNtaV12/rX59AhwAvHnx2FY9MX0P/bq2JnPd4ncX5e8PbezBjaAAf/XyZCeuPkpiax8pxnXG1t6qyfk5RKRsOXmHy5mM8se4I/0tIYe4D7Qlp5Wqok5RRyPJvExn/8RGe2RLHjewi3hkXhItdZZtHk7J49ctTjPswhvAvTuHtYsvrowLrPN5fKfH13rtnN28ti+CZ56aybccXtGvXnmefmUR6enqV9eOOxTLnpVmMHjOW7Tt3MWToMF54fiqJiecq4/l4LZ9+spm5Cxay5dPPsLOz49kpkyguLjbUCZ/9IhfOn2fNR+t5N3INsUeOsHjh/KpOWSeU+h6vDZXKdJs5MOsEfeybz+k08F4CB4zA3duXoaHTsbS24dRP31RZf8SUOQQNfQiPlgG4ebVk2MSZ6PV6rp46BlRcZcd9t4teDz1GQNe+aHz8uefpl8nPSudi7AEAMq4nceXEEYY9NZNmAe1p3rYTg8Y/x7mY/eRlVv0BYkrTnxjK+s8PsPmrQ5y5mMLzS7dRWFTChFF9qj1Gj56b6bmGLTXD+Ip86uNDeGPtN/xvXwInEq/z9LxNeHk4M3JIFwDatfJkRL+OPLd4K4dPXOFA3EXC3tjB30d0w8vDuU7j/dVjvVrw5fEbfJ1wk8vpBbyxN5GiUh0PBjWrsn5sUjb7z6VzOb2A5KwiPjuSzIXUPLq0qOzvt6dSOXwli+vZRVzSFrAy6gJNbC1p3bRyxLTtcDInr+eSklNMQnIOmw9dpZO3Exb1dDNMia/35o3rGTP2UUaNfoSA1q2Zu2ARtra27Pr8P1XW/2TLJvr2H8BT/3wa/4AApk1/gQ6BgWzbugWo+Lv+ZPMmJj/zLEOGDqdtu/a8FrGMtNRUfoj6HoCLFy7wy88/sWDxawQFdaFb9x7MeWUue/d8TWrqzTqPGZT7Hq8NlQk3c3DXCfqnn37iiSeeoE+fPiQnJwOwefNmfv75Z5N17k7Ky0pJvZKIT2A3Q5lKrcYnsCs3LpyqURtlxcXoysuwdXAEICcthYLsDKM2bewd8PRvz40LpwG4ceE0NvZN8GzV1lCnZWA3VCoVNy+eMUVo1bKytKBrBx9+iD5rKNPr9fwQfZZeQa2qPa6JnQ1ndy8mcc8SPnt7Ch38K//g/bzd8fJw5ofoyr7n5BVx+MRlQoL8AAgJakVmTgGxp5IMdX6IPotOp6dnJ18TRlg1S7WKds0cOXw501CmBw5fzqSzt1ON2ujh60JLN3virmZXe45RwV7kFpWRmJpXZR0nW0tGdGxKwrUcynX6WsdRW0p8vUtLSjh96iS9+/Q1lKnVanr37kv88WNVHhMfF0fv3sYXLH379Sc+Lg6A5GvX0GrTCOld2aajoyOdg7oY2jx+/BiOTk507NTZUCekT1/UajUJ8fGmCq9aSn2P15ZapTLZZg7u6h70f/7zH5588knGjx/PsWPHDNNE2dnZvP766+zevfuOxxcXFxtNLd2Nwtwc9Dod9k4uRuX2Tq5k3rhaozZ+2fkxDi7u+HSsSMgFORm32vh9my4UZFfsK8jOwM7ReL/awgJbB0fybx1fVzSuTbC0tLhtRJSankM7P88qj0m8ksoziz7hxLlknBzteOHJYfy4YRbdxy4lOTWLZpqKP/7b28zF071in6e7E2m/219eriMjpwBPTc0+PP4MF3srLNUqMvJLjcoz80vxc7ev9jgHGwv+O7UP1hYqyvXw5reJxPzmAxCgX4AbSx4OxNZKjTavhOnb4skuLDOqM3VwK8Z288bO2oKE5Bxm7UgwXXB3oMTXOzMrk/Lyctzd3Y3K3d3duXTpYpXHaLVa3N01t9XXpmtv7a+4t+6uub1NrbaiTrpWi5ubm9F+S0tLnJydSdemUdeU+h4Xd3ZXI+jXXnuNNWvWsHbtWqysKu9l9OvXj9jY2D88PiIiAmdnZ6Otvh35ejvnYvbx4LT5WFpZ1/v560t0/CW2/i+G+HPJ/Hz0PP94cS3azDwmje3X0F2rcwXF5YSuO8LEjbF88H+XmDE0gG4tjd9rR5OyCF13hMmbj3HoYgZLR3W47Z7fluirhK4/yvRt8eh0ehY8WPUixMZAya+3EintPS5T3DVw9uxZBg4ceFu5s7MzWVlZf3h8eHg42dnZRltt2Tk6oVKrb1sQVpCTib2za9UH3RK7dwdHdm9nVFgEGh9/Q7m9k9utNn7fZhb2zhX77J3dKMw13q8rL6coPxcHJ+MrcFPTZuZRVlZOUzdHo/Km7k6kpOfUqI2yMh3Hz14lwMcDgBRtxXG3t+nIzVtt3kzPweN3+y0s1Lg52XNTW7Pz/hlZBaWU6fS4ORh/qLg6WJGeX/1KUz1wLauIxNR8tsZc48ezaYT2bmlUp6hUx7WsIk5ez+X1Peco1+l56Hf3/LILy7iaWUjM5UzmfnWKfq3d6dS87mcOlPh6u7q4YmFhcduCsPT0dDQaTZXHaDQa0tO1t9e/NarWaCpiT9dW36a7RkNGhvEMWFlZGTnZ2bjfOr4uKfU9XmsKy9B3laCbNWvG+fPnbyv/+eef8ff3r+IIYzY2Njg5ORlttWVhaUVT3zZcPV15X0qv03H1dBxeAdWvQDy65zNi/ruVh8OWGt1HBnDyaIa9s5th0RhAcWE+Ny+ewSugAwBeAR0oLsgj9XKioc7V03Ho9Xo8q/l6l6mUlpVz7PRVhoS0M5SpVCqG9GpLTPylGrWhVqvo2Lq54YP6cnI6N9Kyjdp0dLClZyc/ouMvAxWjMlcne7p28DHUGdyzLWq1isMnqv66jymV6fScTcmlp1/lhZcK6OnrSkJyzROGSgXWlnd+y6tUqjvW+fXelbVl3f+FK/H1trK2pkNgR6IPHTSU6XQ6oqMPEtSla5XHBAUHE33okFHZoYMHCAoOBsC7RQs0Gg+ioyvbzMvLIyH+uKHNLl26kpuTw6mTJwx1YqIPodPp7vj1LlNR6ntc3Nld3YOePHkyM2bMYN26dahUKq5fv87Bgwd58cUXmTdvnqn7WK2uI8bw3Udv4enXFs9W7Yj77gvKiosI7H8PAN+uXYaDq4Z+Y/8JwJHd2zm0azP3TpmNk8aT/Fv3la1s7LC2tUOlUhH8t1Ec/t+nuHh64+TRjENfbMTBxR3/bhULTNyat8S3Uw+iNqxkSOjz6MrL2f9JJG17DaKJq3vVHTWhd7f8wNrFT3L0VBJHTlxm2uNDsLezYdOXFR9QHy15kuup2cx/7ysAwqfcS0z8ZS5cTcPF0Y6ZE4bT0suN9V8cMLQZufVHZj99L+eT0ricnM6C5x7gRlo2X/14HICzl27yzS8niZz3ONOXbsPK0oK35zzKjm9iuZFW+9mPu/FpzDXmPdie0zdyOXUjl3E9vLG1VvN1fAoA8x9sR1puCe/vr0hcob19OJOSx7XMQqwt1fQNcOO+jp4s+6biwsrWSs1TfXz56byW9LwSnO2sGNu9OR6ONkSdqbjn2NHLkQ5ejhy/lk1uURnernY8M8CPq5mFtfrQ/DOU+Ho/OWEi816ZTceOnejUOYgtmzdSWFjIqNFjAHg1/GWaNvVkxsxZAIx/IpRJTz3Jxg3rGDhwEHv37ObkiRPMW7gYqEhI458MZe0H7+Pb0hfvFi2IfO8dPJo2Zeiw4QD4BwTQr/8AFi2Yx9z5iygrKyVi6RLuve8Bmjat+n6/qSn1PV4b8qCSGpgzZw46nY5hw4ZRUFDAwIEDsbGx4cUXX+T55583dR+r1bbXYApzszm0axP52Zl4+Pjz8Mylhinu3Iw0VOrKK8WEH79GV1bK7tWvGbXTa+QT9B5V8XCH7vc9SllxET9sfKfiQSVtOvJw2FKj+9Qjpsxm3yeRfPHmHFTqXx9U8lw9RAw7v41F49qE+c8+gKe7I/Fnk3l4aqRh0Y9PMzd0v1l96epoz+r5j+Pp7khmTiHHTicx5KkVnLmYYqizfMP32NvZsGruY7g42nEg7gIjp66muKRyIcnEVzby9pxH2f3B8+h0FQ+umLVsR73EDPD9mTRc7K2YPMAPdwdrElPzmLk9gYyCikU1zZxs0f9m0amdlQUv3dMaD0cbist0XEkvYOF/z/D9rQ8mnU6Pn7sd93fuiIudFdmFpZxOyeVfW+K4pC0AoKhMx+B2GiYP8MPWyoL0vGIOXcxk/YFTlJbXzwpXJb7e9953P5kZGaxe9S5abRrt2ndg9Qcf4X5rOjrlxg3Uqsq/6+Cu3YhY9har3l3JeytX0NLXj5XvRdKmTeUM2cRJkyksLGTxwvnk5ubQtVt3Vn/wETY2NoY6EW+8RcTSJUyZNMHwoJI54XPrJWZQ7nu8Nsxk8bXJqPR6/V2/CiUlJZw/f568vDwCAwNp0qT6hyf8YUdUKlb9XLNpu7+Caf0rviZjGzy1gXtSv4riIgEIidjXsB2pZ9HhgwFlvd6/vtaFpY3vg74u2VlVZBElvcejwwfzJ1JJjcVcNN0MTi//+l+cXFt/6lGf1tbWBAY2zifOCCGE+GtR2ADa/J/FLYQQQiEUlqHN+lGfQgghxF+VjKCFEEKYBVnFLYQQQjRCSlvFLQlaCCGEWVBYfpZ70EIIIURjJCNoIYQQ5kFhQ2hJ0EIIIcyC0haJyRS3EEII8QciIyPx8/PD1taWkJAQYmJiqq178uRJHnnkEfz8/FCpVKxcufKuzikJWgghhFlQqUy31cb27dsJCwtjwYIFxMbG0qVLF0aMGEFqamqV9QsKCvD39+ff//43zZo1q7JOTUiCFkIIYRZM+XPQxcXF5OTkGG3FxcVVnnfFihVMnjyZiRMnEhgYyJo1a7C3t2fdunVV1u/Zsydvvvkm//jHP4x+kKW2JEELIYRQnIiICJydnY22iIiI2+qVlJRw9OhRhg8fbihTq9UMHz6cgwcP3lbflGSRmBBCCPNgwjVi4eHhhIWFGZVVNdrVarWUl5fj6Wn8u+Cenp6cOXPGdB2qgiRoIYQQZsGUq7htbGz+1PRzfZApbiGEEKIaGo0GCwsLbt68aVR+8+bNP7UArCYkQQshhDALDbGK29ramu7duxMVFWUo0+l0REVF0adPnzqIspJMcQshhDALDfWYkrCwMCZMmECPHj3o1asXK1euJD8/n4kTJwIQGhqKt7e3YZFZSUkJp06dMvx3cnIycXFxNGnShNatW9f4vJKghRBCmIcGytDjxo0jLS2N+fPnk5KSQnBwMHv37jUsHEtKSkKtrpyQvn79Ol27djX8+6233uKtt95i0KBB7Nu3r8bnlQQthBBC/IFp06Yxbdq0Kvf9Pun6+fmh1+v/9DklQQshhDALSnsWtyRoIYQQZqG2j+g0d7KKWwghhGiEZAQthBDCLChsAI1Kb4o72SagUtrchRBC/IXURyo5fSPfZG118HIwWVt1Raa4hRBCiEaoUU1xr/r5UkN3od5M698KgMLSRjGBUW/srCpmSiTuvz4lxgzKjPvXmOuarOIWQgghGiGl3QmVKW4hhBCiEZIRtBBCCLOgsAG0JGghhBBmQmEZWhK0EEIIs6C0RWJyD1oIIYRohGQELYQQwiwobRW3JGghhBBmQWH5Waa4hRBCiMZIRtBCCCHMg8KG0JKghRBCmAVZxS2EEEKIBicjaCGEEGZBVnELIYQQjZDC8rNMcQshhBCNkYyghRBCmAeFDaElQQshhDALSlvFLQlaCCGEWVDaIjG5By2EEEI0QjKCFkIIYRYUNoCWBC2EEMI8yBS3EEIIIRqcjKCFEEKYCWUNoc1+BH086ivWvxRK5JQH2b5kOikXz1Rb98T+3eyMCOODaY/wwbRH+OLN2bfV1+v1HPpiIx/NfIzIZx7iizdnk3Uz2ahOUV4O33z4b95/bjRrpo7h+3UrKCkqrJP4qrJt6yfc97eh9OzamfH/+DsJ8fF3rP/tN3t4+MF76dm1M4+Meoif/m+/0X69Xk/ke+8wbFB/enULYsqkp7hy5bJRneysLMJfnkXfXt3o37sHC+a9QkF+vqlDuyOJWzlxKzFmUG7cNaVSmW4zB2adoM/F7OOn7R8SMnI8/1gQicbHny9XvEpBTlaV9ZPPxtM2ZAhjXl7G3199myZuHuxa/gp5mVpDnaN7PiPu+y8ZEvo84+a+g6WNLbuWv0JZaYmhzjcfvkF68hVGz4pg5IzFJJ9L4IeNK+s42gp79+zmrWURPPPcVLbt+IJ27drz7DOTSE9Pr7J+3LFY5rw0i9FjxrJ95y6GDB3GC89PJTHxnKHO+o/X8uknm5m7YCFbPv0MOzs7np0yieLiYkOd8NkvcuH8edZ8tJ53I9cQe+QIixfOr/N4fyVxKyduJcYMyo1bVM+sE/Sxbz6n08B7CRwwAndvX4aGTsfS2oZTP31TZf0RU+YQNPQhPFoG4ObVkmETZ6LX67l66hhQcbUZ990uej30GAFd+6Lx8eeep18mPyudi7EHAMi4nsSVE0cY9tRMmgW0p3nbTgwa/xznYvaTl1n1H5Ipbd64njFjH2XU6EcIaN2auQsWYWtry67P/1Nl/U+2bKJv/wE89c+n8Q8IYNr0F+gQGMi2rVsMMX+yeROTn3mWIUOH07Zde16LWEZaaio/RH0PwMULF/jl559YsPg1goK60K17D+a8Mpe9e74mNfVmnccscSsrbiXGrOS4a0Nlws0cmG2CLi8rJfVKIj6B3QxlKrUan8Cu3LhwqkZtlBUXoysvw9bBEYCctBQKsjOM2rSxd8DTvz03LpwG4MaF09jYN8GzVVtDnZaB3VCpVNy8w/S6KZSWlHD61El69+lrKFOr1fTu3Zf448eqPCY+Lo7evfsYlfXt15/4uDgAkq9dQ6tNI6R3ZZuOjo50DupiaPP48WM4OjnRsVNnQ52QPn1Rq9V/OAVnChK3cuJWYsyg3LhrS6a4qxAfH49OpzPZSYuLi8nJyTHaaqswNwe9Toe9k4tRub2TKwXZmTVq45edH+Pg4o5Px4qEXJCTcauN37fpQkF2xb6C7AzsHI33qy0ssHVwJP/W8XUlMyuT8vJy3N3djcrd3d3RarVVHqPVanF319xeP117a39aRZmm+jbTtVrc3NyM9ltaWuLk7Ez6rePrksStnLiVGDMoN25xZzVK0F27djW8oP7+/tXeE6mpiIgInJ2djbb6duTr7ZyL2ceD0+ZjaWVd7+cXQghROyoT/s8c1ChBu7i4cOnSJQAuX778p0fT4eHhZGdnG221ZefohEqtvm1BWEFOJvbOrnc8NnbvDo7s3s6osAg0Pv6Gcnsnt1tt/L7NLOydK/bZO7tRmGu8X1deTlF+Lg5Oxleipubq4oqFhcVtF0jp6eloNJoqj9FoNKSna2+vf+vKW6PxqCjTVt+mu0ZDRobx7EBZWRk52dm43zq+LkncyolbiTGDcuOuNYXdhK5Rgn7kkUcYNGgQrVq1QqVS0aNHD/z9/avcasLGxgYnJyejrbYsLK1o6tuGq6cr78/odTquno7DKyCw2uOO7vmMmP9u5eGwpUb3kQGcPJph7+xmWDQGUFyYz82LZ/AK6ACAV0AHigvySL2caKhz9XQcer0eT//2tY6jNqysrekQ2JHoQwcNZTqdjujogwR16VrlMUHBwUQfOmRUdujgAYKCgwHwbtECjcaD6OjKNvPy8kiIP25os0uXruTm5HDq5AlDnZjoQ+h0OjoHBZkqvGpJ3MqJW4kxg3Ljri2F5eeaPajkww8/ZMyYMZw/f57p06czefJkHB0d67pvf6jriDF899FbePq1xbNVO+K++4Ky4iIC+98DwLdrl+HgqqHf2H8CcGT3dg7t2sy9U2bjpPEk/9Z9ZSsbO6xt7VCpVAT/bRSH//cpLp7eOHk049AXG3Fwcce/W8VCC7fmLfHt1IOoDSsZEvo8uvJy9n8SSdteg2ji6l51R03oyQkTmffKbDp27ESnzkFs2byRwsJCRo0eA8Cr4S/TtKknM2bOAmD8E6FMeupJNm5Yx8CBg9i7ZzcnT5xg3sLFAKhUKsY/GcraD97Ht6Uv3i1aEPneO3g0bcrQYcMB8A8IoF//ASxaMI+58xdRVlZKxNIl3HvfAzRt6lnnMUvcyopbiTErOW5RvRo/Sezee+8F4OjRo8yYMaNRJOi2vQZTmJvNoV2byM/OxMPHn4dnLjVMcedmpKFSV04SJPz4NbqyUnavfs2onV4jn6D3qCcB6H7fo5QVF/HDxncoLsijeZuOPBy21Og+9Ygps9n3SSRfvDkHlVpF6+79Gfj4c/UQMdx73/1kZmSwetW7aLVptGvfgdUffIT7rSmrlBs3UKsqYw7u2o2IZW+x6t2VvLdyBS19/Vj5XiRt2lTOHkycNJnCwkIWL5xPbm4OXbt1Z/UHH2FjY2OoE/HGW0QsXcKUSRNQq9UM+9s9zAmfWy8xS9zKiluJMSs57towl9XXpqLS6/X6hu4EVFztrfr5UkN3o95M698KgMLSRvF/f72xs6r4C5O4//qUGDMoM247KxX1kUrScstM1paHY+N/0rXZfg9aCCGE+Ctr/JcQQgghBJjP6i4TkQQthBDCLCgsP8sUtxBCCNEYyQhaCCGEWVDaKm5J0EIIIcyCuTyi01RkilsIIYRohGQELYQQwiwobYpbRtBCCCFEIyQjaCGEEGZBRtBCCCGEaHAyghZCCGEWlLaKWxK0EEIIsyBT3EIIIYRocDKCFkIIYRYUNoCWBC2EEMJMKCxDyxS3EEII0QjJCFoIIYRZkFXcQgghRCMkq7iFEEII0eBkBC2EEMIsKGwALQlaCCGEmVBYhpYpbiGEEGZBZcL/1VZkZCR+fn7Y2toSEhJCTEzMHevv2LGD9u3bY2trS+fOndm9e3etzykJWgghhLiD7du3ExYWxoIFC4iNjaVLly6MGDGC1NTUKusfOHCAxx57jEmTJnHs2DFGjRrFqFGjOHHiRK3Oq9Lr9XpTBPBnqZS2PE8IIf5C6iOVFJWZri1VeTHFxcVGZTY2NtjY2NxWNyQkhJ49e7Jq1SoAdDodPj4+PP/888yZM+e2+uPGjSM/P5///e9/hrLevXsTHBzMmjVratzHRjOC1uv1DbIVFRWxYMECioqKGqwPErPELTFL3OYed32wtTTdFhERgbOzs9EWERFx2zlLSko4evQow4cPN5Sp1WqGDx/OwYMHq+znwYMHjeoDjBgxotr61Wk0I+iGkpOTg7OzM9nZ2Tg5OTV0d+qFEmMGZcatxJhB4lZa3HejuLhmI+jr16/j7e3NgQMH6NOnj6H85ZdfZv/+/URHR9/WtrW1NRs3buSxxx4zlK1evZpFixZx8+bNGvdRVnELIYRQnOqmsxuTRjPFLYQQQjQ2Go0GCwuL20a+N2/epFmzZlUe06xZs1rVr44kaCGEEKIa1tbWdO/enaioKEOZTqcjKirKaMr7t/r06WNUH+C7776rtn51FD/FbWNjw4IFCxr9VIcpKTFmUGbcSowZJG6lxV3XwsLCmDBhAj169KBXr16sXLmS/Px8Jk6cCEBoaCje3t6GRWYzZsxg0KBBLF++nAceeIBt27Zx5MgRPvzww1qdV/GLxIQQQog/smrVKt58801SUlIIDg7m3XffJSQkBIDBgwfj5+fHhg0bDPV37NjB3LlzuXz5Mm3atGHZsmXcf//9tTqnJGghhBCiEZJ70EIIIUQjJAlaCCGEaIQkQQshhBCNkCRoBRk8eDAvvPBCQ3dDNCB5D/x16fV6pkyZgpubGyqViri4uIbukviTFP81KyGE+CvYu3cvGzZsYN++ffj7+6PRaBq6S+JPkgQthBB/ARcuXMDLy4u+ffs2dFeEiSh2invv3r30798fFxcX3N3defDBB7lw4UJDd6vOlZWVMW3aNJydndFoNMybN6/efommIel0OpYtW0br1q2xsbGhZcuWLF26tKG7Vafy8/MJDQ2lSZMmeHl5sXz58obuUp3T6XRERETQqlUr7Ozs6NKlCzt37mzobtW5p556iueff56kpCRUKhV+fn4N3SVhAopN0Pn5+YSFhXHkyBGioqJQq9WMHj0anU7X0F2rUxs3bsTS0pKYmBjeeecdVqxYwUcffdTQ3apz4eHh/Pvf/2bevHmcOnWKrVu34unp2dDdqlMvvfQS+/fv58svv+Tbb79l3759xMbGNnS36lRERASbNm1izZo1nDx5kpkzZ/LEE0+wf//+hu5anXrnnXdYvHgxLVq04MaNGxw+fLihuyRMQS/0er1en5aWpgf0CQkJDd2VOjNo0CB9hw4d9DqdzlA2e/ZsfYcOHRqwV3UvJydHb2Njo1+7dm1Dd6Xe5Obm6q2trfWfffaZoSw9PV1vZ2ennzFjRsN1rA4VFRXp7e3t9QcOHDAqnzRpkv6xxx5roF7Vn7ffflvv6+vb0N0QJqTYEXRiYiKPPfYY/v7+ODk5GaaEkpKSGrZjdax3796oVCrDv/v06UNiYiLl5eUN2Ku6dfr0aYqLixk2bFhDd6XeXLhwgZKSEsOjCAHc3Nxo165dA/aqbp0/f56CggL+9re/0aRJE8O2adMmRdy+En89il0k9tBDD+Hr68vatWtp3rw5Op2OTp06UVJS0tBdEyZmZ2fX0F0Q9SAvLw+Ar7/+Gm9vb6N98uMRwhwpcgSdnp7O2bNnmTt3LsOGDaNDhw5kZmY2dLfqRXR0tNG/Dx06RJs2bbCwsGigHtW9Nm3aYGdnd9vPv/2VBQQEYGVlZfR6Z2Zmcu7cuQbsVd0KDAzExsaGpKQkWrdubbT5+Pg0dPeEqDVFjqBdXV1xd3fnww8/xMvLi6SkJObMmdPQ3aoXSUlJhIWF8cwzzxAbG8t77733l1/da2try+zZs3n55ZextramX79+pKWlcfLkSSZNmtTQ3asTTZo0YdKkSbz00ku4u7vTtGlTXn31VdTqv+41uaOjIy+++CIzZ85Ep9PRv39/srOz+eWXX3BycmLChAkN3UUhakWRCVqtVrNt2zamT59Op06daNeuHe+++y6DBw9u6K7VudDQUAoLC+nVqxcWFhbMmDGDKVOmNHS36ty8efOwtLRk/vz5XL9+HS8vL/71r381dLfq1JtvvkleXh4PPfQQjo6OzJo1i+zs7IbuVp1asmQJHh4eREREcPHiRVxcXOjWrRuvvPJKQ3dNiFqTn5sUQgghGqG/7nyXEEIIYcYkQQshhBCNkCRoIYQQohGSBC2EEEI0QpKghRBCiEZIErQQQgjRCEmCFkIIIRohSdBCCCFEIyQJWgghhGiEJEELIYQQjZAkaCGEEKIR+n+ZQpH9D3sHIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(T_2, cmap = 'Blues', \n",
    "            annot = True, fmt = '.3f',\n",
    "            xticklabels = list(directed_G.nodes), \n",
    "            yticklabels = list(directed_G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('转移矩阵，删除ea.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3c96103-dd90-481b-b25c-3b661c1d7f00",
   "metadata": {},
   "source": [
    "## 幂迭代修正"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "9a75d8e8-64e6-4267-abf6-a280df2e4377",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 幂迭代，修正\n",
    "\n",
    "def power_iteration_adjust(T_, num_iterations: int, d = 0.85, \n",
    "                           tol=1e-6, L2_norm = False):\n",
    "    \n",
    "    n = len(T_)\n",
    "    # 初始状态\n",
    "    r_k = np.ones((len(T_),1))/n\n",
    "    r_k_iter = r_k\n",
    "\n",
    "    # 幂迭代过程\n",
    "    for _ in range(num_iterations):\n",
    "        \n",
    "        # 核心迭代计算式\n",
    "        r_k1 = d * T_ @ r_k + (1-d)/n \n",
    "\n",
    "        # 检测是否收敛\n",
    "        if np.linalg.norm(r_k - r_k1, 1) < tol:\n",
    "            break\n",
    "\n",
    "        if L2_norm:\n",
    "            # 计算L2范数\n",
    "            r_k1_norm = np.linalg.norm(r_k1)\n",
    "\n",
    "            # L2范数单位化\n",
    "            r_k = r_k1 / r_k1_norm\n",
    "        else:\n",
    "            # 归一化\n",
    "            r_k = r_k1 / r_k1.sum()\n",
    "        \n",
    "        # 记录迭代过程结果\n",
    "        r_k_iter = np.column_stack((r_k_iter,r_k))\n",
    "\n",
    "    return r_k,r_k_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "230b12b9-d3fe-40cf-8ede-f1a999e22bf9",
   "metadata": {},
   "outputs": [],
   "source": [
    "r_k_adj,r_k_iter_adj = power_iteration_adjust(T_2, 20, 0.85)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "56210ed9-8dfe-492f-9e9f-b85f49b509ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.06822847],\n",
       "       [0.21109448],\n",
       "       [0.07597197],\n",
       "       [0.2168053 ],\n",
       "       [0.37422838],\n",
       "       [0.05367139]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_k_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "132fc77c-91ae-41b8-90e8-b556adf634c0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "80b5a2f8-34fd-46ef-b5d7-f82b6dc1279c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 可视化幂迭代过程\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "for i,node_i in zip(range(len(node_color)),list(directed_G.nodes)):\n",
    "    ax.plot(r_k_iter_adj[i,:], color = node_color[i], label = node_i)\n",
    "ax.set_xlim(0,20)\n",
    "ax.set_ylim(0,0.4)\n",
    "ax.set_xlabel('Iteration')\n",
    "ax.set_ylabel('PageRank')\n",
    "ax.legend(loc = 'upper right')\n",
    "plt.savefig('幂迭代，修正.svg')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
